Evaluation of the risk due to fluvial flooding in vehicles

Universitat Politècnica de València Departamento de Ingeniería Hidráulica y Medio Ambiente

Programa de Doctorado de Ingeniería del Agua y Medioambiental

Evaluation of the risk due to fluvial flooding in vehicles and road infrastructures at basin scale

AUTHOR: RICARDO ANDRÉS BOCANEGRA VINASCO. SUPERVISORS: DR. FÉLIX FRANCÉS GARCÍA . DR. FRANCISCO JOSÉ VALLÉS MORÁN

VALENCIA, JULY 2020

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Universitat Politècnica de València Departamento de Ingeniería Hidráulica y Medio Ambiente

Programa de Doctorado de Ingeniería del Agua y Medioambiental

Evaluation of the risk due to fluvial

flooding in vehicles and road

infrastructures at basin scale

AUTHOR: RICARDO ANDRÉS BOCANEGRA VINASCO. SUPERVISORS: DR. FÉLIX FRANCÉS GARCÍA .

DR. FRANCISCO JOSÉ VALLÉS MORÁN VALENCIA, JULY 2020

Acknowledgements .

ACKNOWLEDGEMENTS

I would like to thank professors Félix Francés García and Francisco José Vallés Morán for their

advice, suggestions and guidance in conducting this research.

I would like to thank my colleagues in the GIHMA group, especially Shantosa and Claudia,

who offered me their friendship during this period.

I also thank Colciencias for financing this research through call 728-2015.

Quisiera agradecer a María, mi esposa, por su acompañamiento y apoyo incondicional en todo

momento y a Sarita, mi hija, por entender que yo también tenía que hacer deberes. También

quisiera agradecer a mis padres por sus enseñanzas. Finalmente, no encuentro palabras para

manifestar mi agradecimiento a mi tía, sin su apoyo firme y decidido no hubiera podido recorrer

el camino que me ha traído hasta aquí.

Table of contents .

TABLE OF CONTENTS

1 INTRODUCTION ............................................................................................................... 1

1.1 General Introduction ................................................................................................ 1

1.2 Objectives ................................................................................................................ 3

1.3 Flood risk ................................................................................................................. 3

1.3.1 Flood hazard ............................................................................................................ 4

1.3.2 Vulnerability ............................................................................................................ 4

1.3.3 Calculation of risk .................................................................................................... 4

1.4 Document structure ................................................................................................. 5

2 REVIEW AND ANALYSIS OF VEHICLE STABILITY MODELS DURING

FLOODS ............................................................................................................................... 7

2.1 Introduction ............................................................................................................. 7

2.2 Description of the studied stability models ............................................................. 7

2.2.1 Stability models that consider non-watertightness of vehicles during floods ......... 8

2.2.2 Stability models that consider vehicle watertightness during floods ....................... 9

2.2.3 Stability models that consider watertightness and non-watertightness of vehicles

during floods .......................................................................................................... 11

2.3 Comparison of vehicle stability thresholds ........................................................... 13

2.3.1 Assuming vehicle watertightness .......................................................................... 13

2.3.2 Assuming vehicle non-watertightness ................................................................... 14

2.4 Comparison of vehicle stability thresholds with experimental data ...................... 15

2.4.1 Experimental data .................................................................................................. 15

2.4.2 Comparison between experimental data and stability models .............................. 16

2.5 Final Remarks ........................................................................................................ 17

3. ASSESSING THE RISK OF VEHICLE INSTABILITY DUE TO FLOODING ....... 20

3.1 Introduction ........................................................................................................... 21

3.2 Vehicle stability in flooded areas .......................................................................... 21

3.3 Methodology to estimate the vehicle instability risk using formal statistics ........ 23

3.3.1 Vehicle instability hazard ...................................................................................... 24

3.3.2 Vulnerability .......................................................................................................... 25

3.3.3 Vehicle Instability Risk ......................................................................................... 25

3.4 Applying a case study ........................................................................................................ 27

3.4.1 Description of the study area ................................................................................. 27

Table of contents .

3.4.2 Characterization and exposure of the vehicles in the study area ........................... 27

3.4.3 Vehicle stability thresholds ................................................................................... 28

3.4.4 Vulnerability .......................................................................................................... 29


3.4.6 Vehicle instability risk ........................................................................................... 32

3.4.7 Sensitivity analysis to Tmin .................................................................................. 34

3.4.8 Final Remarks ........................................................................................................ 35

4. DETERMINING THE VEHICLE INSTABILITY RISK IN STREAM

CROSSINGS ...................................................................................................................... 37

4.1 Introduction ........................................................................................................... 37

4.2 Methodology ......................................................................................................... 37


4.2.2 Vulnerability .......................................................................................................... 38

4.2.2.1 Susceptility ..................................................................................................... 38

4.2.2.2 Exposure ........................................................................................................ 38


4.3 Application to a case study ............................................................................................... 42

4.3.1 Characterisation of the study area ......................................................................... 42

4.3.2 Characterisation and exposure of the vehicles driving through the study area ..... 43


4.3.4 Vulnerability .......................................................................................................... 44


4.3.6 Influence of the limit water depth ......................................................................... 48

4.3.7 Final Remarks ........................................................................................................ 49

5 RISK ASSESSMENT OF BRIDGE FAILURE DUE TO RIVER FLOODS .............. 51

5.1 Introduction ........................................................................................................... 51

5.2 Failure of bridges over water currents ................................................................... 52

5.2.1 Typology of fails ................................................................................................... 52

5.2.2 Causes of failures .................................................................................................. 52

5.3 Methodology ......................................................................................................... 53

5.3.1 Hazard ................................................................................................................... 53

5.3.2 Vulnerability .......................................................................................................... 54

5.3.2.1 Base vulnerability .......................................................................................... 55

5.3.2.2 Stream channel stability ................................................................................. 57

5.3.2.3 Potential of the structure to accumulate debris .............................................. 58

Table of contents .

5.3.2.4 Deterioration of the structure due to its age and the environment in which

it is located ..................................................................................................... 60

5.3.3 Risk of bridge failure due to river floods .............................................................. 63

5.4 Application in a case study .................................................................................... 63

5.5 Sensitivity analysis ................................................................................................ 67

5.6 Final Remarks ........................................................................................................ 68

6 CONCLUSIONS AND FUTURES RESEARCH LINES .............................................. 69

6.1 Conclusions ........................................................................................................... 69

6.1.1 Vehicle stability models during floods .................................................................. 69

6.1.2 Assessing the risk of vehicle instability due to flooding ....................................... 70

6.1.3 Determining the vehicle instability risk in stream crossings ................................. 70

6.1.4 Risk assessment of bridge failure due to river floods ........................................... 71

6.2 Futures research lines ............................................................................................ 72

REFERENCES

.

List of figures .

LIST OF FIGURES

Figure 1.1 Diagram illustrating the process that must be implemented to calculate the risk .... 3

Figure 1.2 Damage - probability curve ..................................................................................... 5

Figure 2.1 Stability thresholds for vehicles in flood events .................................................... 12

Figure 2.2 Comparison of vehicle stability thresholds during floods proposed by stability

models that consider car watertightness ................................................................................... 13

Figure 2.3 Comparison of vehicle stability thresholds during floods proposed by models that

consider large 4WD vehicles and car non-watertightness ....................................................... 14

Figure 2.4. Comparison of proposed stability thresholds for vehicles under watertight

conditions during floods with experimental data ..................................................................... 16

Figure 3.1 Geometry of the car used to determine mobility parameter θv. ............................. 22

Figure 3.2 Diagram of the mobility parameter θv vs Froude number. .................................... 23

Figure 3.3 Diagram illustrating the process that must be implemented to calculate the

instability hazard in one vehicle i ............................................................................................. 24

Figure 3.4 Diagram of the instability risk of a single vehicle type i ........................................ 26

Figure 3.5 Location of the Rambla del Poyo basin and the study area ................................... 27

Figure 3.6 Stability thresholds for each vehicle type .............................................................. 29

Figure 3.7 Flood hazard: maximum water depths and their corresponding flow velocities in

the study area due to the la Rambla del Poyo flooding with a 100-year return period ............ 30

Figure 3.8 Hazard maps of vehicle instability in the study area for floods with return periods

of 50 and 500 years for Seat Ibiza ............................................................................................ 31

Figure 3.9 Risk map of instability for each vehicle type studied in the study area without

considering their proportion in the vehicle fleet ...................................................................... 33

Figure 3.10 Map of the instability risk for vehicles in the study area ...................................... 34

Figure 3.11 Number of cars at risk of instability in the study area when considering different

Tmin values .............................................................................................................................. 35

Figure 4.1 Outline of the process to follow to determine the exposure function of vehicles

type i ......................................................................................................................................... 39

Figure 4.2 Outline of the procedure to follow to obtain vulnerability of vehicles type i in the

event of floods .......................................................................................................................... 40

Figure 4.3 Outline of the process that must be set up to calculate the instability risk for

flooding vehicles type i in a stream crossing ........................................................................... 41

Figure 4.4 Location of the Godelleta municipality, ravines, main roads ................................ 42

Figure 4.5 Vehicle instability risk due to floods in the stream crossings in the Godelleta

municipality .............................................................................................................................. 47

List of figures .

Figure 4.6 Number of vehicles at instability risk in the Godelleta municipality by considering

different water depth values from which vehicle traffic could cease ....................................... 48

Figure 5.1 Scheme representing the bands into which the cross section of a watercourse is

divided for the purpose of the magnitude of a flood ................................................................ 54

Figure 5.2 Location of the bridges to which the methodology was applied ........................... 64

List of tables .

LIST OF TABLES

Table 2.1 Studied models for the determination of vehicle stability ...................................... 19

Table 3.1 Characteristics of the vehicles in the study area ..................................................... 28

Table 3.2 Mean annual number of at-risk vehicles for instability in the whole study area in

line with the two fleet hypotheses: only one type and with the present proportion ............... 34

Table 4.1 Vehicle instability risk due to floods in the stream crossings of the Godelleta

municipality .............................................................................................................................. 46

Table 4.2 Vehicle instability risk by taking a limit water depth of 0.3 m and vented fords with

circular vents and a diameter less than 1.0 m, or equivalent geometries, being unblocked or

completely obstructed .............................................................................................................. 48

Table 5.1 Base vulnerability of the substructure (VBb) and superstructure (VBs) of a bridge

in floods adopted in this proposal ............................................................................................ 56

Table 5.2 Proposed values of the base vulnerability multiplication factor due to the stability of

the water current (Fs) ................................................................................................................ 58

Table 5.3 Proposed values of the base vulnerability multiplication factor due to the potential

of the structure to accumulate debris (Fd) ................................................................................ 59

Table 5.4 Proposed values of the base vulnerability multiplication factor due to the

deterioration of the bridge structure (Ft) .................................................................................. 62

Table 5.5 Specifications of the bridges to which the developed methodology was applied ... 64

Table 5.6 Stability of water currents and condition of the structures of the bridges

analysed ................................................................................................................................... 65

Table 5.7 Risk of failure of bridges located on Spanish roads due to river floods ................. 66

Table 5.8 Fail Risk Sensitivity Test ....................................................................................... 68

Abstract .

ABSTRACT

Flooding can destabilize vehicles which might, in turn, exacerbate the negative effects of floods

when vehicles are swept away by flows, leading to economic loss and fatalities. The main cause

of death in cities during flood events corresponds to cars being swept away when they are driven

by flooded roads (Jonkzman and Kelman 2005; Drobot et al. 2007; Kellar and Schmidlin 2012).

In developed countries a high percentage of these deaths occurs during flash floods when

drivers try to cross overflowing water bodies instead of avoiding them (Fitzgerald et al. 2010;

Kellar and Schmidlin 2012). Hence, in areas subject to flash floods almost half of the victims

are passengers trapped inside their own vehicles (Versini et al. 2010a).

Among the parts of the roads that are most affected by floods are bridges, which are very

important infrastructure works for society. Because of this, a high percentage of bridge failures

worldwide occur as a result of river floods, which has highly negative impacts for vehicles and

transportation systems.

Therefore, in order to suitably manage floods, it is necessary to determine the risk of instability

to which vehicles in flood-prone areas are subject. However, Despite the negative impact of

floods, very few studies have centred on determining the negative effects of floods on transport

systems (Molarius et al., 2014).

In this research, a new methodology to estimate this risk based on the characteristics of vehicles,

floods, bridges and vehicular traffic was developed. This methodology was generated from a

novel conceptual structure and mathematical development and allows to determine the risk by

the statistical integral of the instability hazard and the vehicles’ vulnerability. In urban areas

and stream crossings, the hazard is determined by a stability criterion of partially submerged

cars, the geometric characteristics of the vehicles and the hydrodynamic characteristics of the

floods (depths and velocities) and their probability of occurrence, while vulnerability is

calculated by combining the susceptibility and exposure of cars.

In bridges, the hazard is obtained by analysing available discharge data and the vulnerability

by examining the structural condition of the bridge, the characteristics of the watershed and

watercourse upstream and downstream of the structure, the stability of the channel and the

potential accumulation of debris.

The developed methodology was implemented to determine the risk in the following case

studies, which are located in Spanish territory: (i) in the urban areas corresponding to the towns

of Alfafar and Massanassa; (ii) in the stream crossings located in the municipality of Godelleta;

and (iii) in 12 river bridges located. The results obtained could be indicating that the proposed

method takes into account the most important elements to be considered when establishing this

type of risk.

The developed methodology provides a detailed vision of the vehicle instability risk due to

flooding in a given area. Consequently, implementing this methodology can help to reduce

negative effects before and during flooding events, which is extremely helpful for those

organizations in charge of urban planning and civil protection to design and take actions that

cushion the negative effects of flooding.

Resumen .

RESUMEN

Las inundaciones pueden llegar a desestabilizar los vehículos y estos, a su vez, pueden

exacerbar los efectos negativos de las inundaciones cuando son arrastrados por el flujo,

generando no solamente pérdidas económicas sino también de vidas humanas. En las ciudades,

la mayor parte de las muertes durante las inundaciones ocurre al interior de los vehículos debido

a que los conductores intentan cruzar con sus vehículos por zonas inundadas (Jonkzman and

Kelman 2005; Drobot et al. 2007; Kellar and Schmidlin 2012). En países desarrollados, un alto

porcentaje de estas muertes ocurre durante inundaciones relámpago cuando los conductores

intentan cruzar por zonas inundadas en lugar de evitarlas (Fitzgerald et al. 2010; Kellar y

Schmidlin 2012). Debido a esto, en áreas sujetas a inundaciones relámpago, casi la mitad de las

víctimas son pasajeros atrapados en sus propios vehículos (Versini et al. 2010a)

Entre las partes de las vías que resultan afectadas por las crecidas de los ríos se encuentran los

puentes, las cuales son obras de infraestructura muy importantes. Un alto porcentaje de los

fallos de los puentes a nivel mundial se presenta como consecuencia de las crecidas de los ríos,

lo cual tiene un impacto altamente negativo en los vehículos y los sistemas de transporte.

Debido a esto, con el fin de realizar una adecuada gestión de las inundaciones es necesario

determinar el riesgo de inestabilidad al que están sometidos los vehículos en una zona

inundable. Sin embargo, a pesar del impacto negativo de las inundaciones, hasta la fecha se

dispone de pocos estudios que permitan determinar los efectos negativos que las condiciones

climáticas generan sobre los sistemas de transporte (Molarius et al., 2014).

En la presente investigación se desarrolló una nueva metodología para calcular este riesgo a

partir de las características de las crecidas, los puentes, los vehículos, y el tráfico vehicular. Esta

metodología fue generada a partir de una estructura conceptual y un desarrollo matemático

novedosos y permite determinar el riesgo a través de la integral estadística de la amenaza de

inestabilidad y la vulnerabilidad de los coches. En áreas urbanas y en las intersecciones entre

las corrientes de agua y las vías, la amenaza se establece a través de una función de estabilidad

de autos parcialmente sumergidos, las características geométricas de los vehículos y las

características hidrodinámicas de las crecidas (calados y velocidades) y su probabilidad de

ocurrencia, mientras que la vulnerabilidad se calcula por medio de la combinación de la

susceptibilidad y la exposición de los coches.

En puentes, la peligrosidad se obtiene a través del análisis de los datos de caudal disponibles y

la vulnerabilidad mediante el análisis del estado estructural del puente, las características de la

cuenca y del cauce aguas arriba y aguas abajo de la estructura, la estabilidad del canal y la

potencial acumulación de acarreos.

La metodología desarrollada se implementó para determinar el riesgo en los siguientes casos

de estudio, los cuales están localizados en territorio español: (i) en las áreas urbanas

correspondientes a los municipios de Alfafar y Massanassa, (ii) en los sitios de intersección

entre vías y ríos localizados en el municipio de Godelleta; y (iii) en 12 puentes fluviales. Los

resultados obtenidos podrían estar indicando que el método propuesto tiene en cuenta los

elementos más importantes que deben considerarse al establecer este tipo de riesgo.

La metodología desarrollada permite obtener un panorama detallado del riesgo de

desestabilización de los vehículos debido a inundaciones en una zona determinada. En

Resumen .

consecuencia, la implementación de esta metodología puede ayudar a disminuir los efectos

negativos antes y durante este tipo de eventos, resultando de gran ayuda para las entidades

encargadas de la planificación urbana y de la protección civil con el fin de diseñar e

implementar acciones que permitan disminuir los efectos negativos de las inundaciones.

Resum .

RESUM

Les inundacions poden desestabilitzar els vehicles i aquests, al mateix temps, poden exacerbar

els efectes negatius de les inundacions quan són arrossegats pel flux, generant no solament

pèrdues econòmiques sinó també de vides humanes. A les ciutats, la major part de les morts

durant les inundacions ocorre a l'interior dels vehicles pel fet que els conductors intenten creuar

amb els seus vehicles per zones inundades (Jonkzman and Kelman 2005; Drobot et al. 2007;

Kellar and Schmidlin 2012). En països desenvolupats, un alt percentatge d'aquestes morts

ocorre durant inundacions llampec quan els conductors intenten creuar per zones inundades en

lloc d'evitar-les (Fitzgerald et al. 2010; Kellar i Schmidlin 2012). A causa d'això, en àrees

subjectes a inundacions llampec, quasi la meitat de les víctimes són passatgers atrapats en els

seus propis vehicles (Versini et al. 2010a)

Entre les parts de les vies que resulten afectades per les crescudes dels rius es troben els ponts,

les quals són obres d'infraestructura molt importants. Un alt percentatge de les fallades dels

ponts a nivell mundial es presenta com a conseqüència de les crescudes dels rius, la qual cosa

té un impacte altament negatiu en els vehicles i els sistemes de transport..

A causa d'això, amb la finalitat de realitzar una adequada gestió de les inundacions és necessari

determinar el risc d'inestabilitat al qual estan sotmesos els vehicles en una zona inundable. No

obstant això, malgrat l'impacte negatiu de les inundacions, fins a la data es disposa de pocs

estudis que permeten determinar els efectes negatius que les condicions climàtiques generen

sobre els sistemes de transport (Molarius et al., 2014).

En la present investigació es va desenvolupar una nova metodologia per a calcular aquest risc

a partir de les característiques de les crescudes, els ponts, els vehicles, i el trànsit vehicular.

Aquesta metodologia va ser generada a partir d'una estructura conceptual i un desenvolupament

matemàtic nous i permet determinar el risc a través de la integral estadística de l'amenaça

d'inestabilitat i la vulnerabilitat dels cotxes. En àrees urbanes i en les interseccions entre els

corrents d'aigua i les vies, l'amenaça s'estableix a través d'una funció d'estabilitat de cotxes

parcialment submergits, les característiques geomètriques dels vehicles i les característiques

hidrodinàmiques de les crescudes (calats i velocitats) i la seua probabilitat d'ocurrència, mentre

que la vulnerabilitat es calcula per mitjà de la combinació de la susceptibilitat i l'exposició dels

cotxes.

En ponts, la perillositat s'obté a través de l'anàlisi de les dades de cabal disponibles i la

vulnerabilitat mitjançant l'anàlisi de l'estat estructural del pont, les característiques de la conca

i del llit aigües amunt i aigües avall de l'estructura, l'estabilitat del canal i la potencial

acumulació d'enderrocs.

La metodologia desenvolupada es va implementar per a determinar el risc en els següents casos

d'estudi, els quals estan localitzats en territori espanyol: (i) en les àrees urbanes corresponents

als municipis d'Alfafar i Massanassa, (ii) en els llocs d'intersecció entre vies i rius localitzats en

el municipi de Godelleta; i (iii) en

12 ponts fluvials. Els resultats obtinguts podrien estar indicant que el mètode proposat té en

compte els elements més importants que han de considerar-se en establir aquest tipus de risc.

La metodologia desenvolupada permet obtindre un panorama detallat del risc de

desestabilització dels vehicles a causa d'inundacions en una zona determinada. En

Resum .

conseqüència, la implementació d'aquesta metodologia pot ajudar a disminuir els efectes

negatius abans i durant aquesta mena d'esdeveniments, resultant de gran ajuda per a les entitats

encarregades de la planificació urbana i de la protecció civil amb la finalitat de dissenyar i

implementar accions que permeten disminuir els efectes negatius de les inundacions.

Chapter 1, Introduction .

1

1 INTRODUCTION

1.1 General Introduction

Floods are a natural phenomenon with major negative impacts on society because they cause

substantial indirect and direct losses that affect people’s lives and health, deteriorate existing

infrastructures and interrupt different public services and productive activities (Yin et al., 2016).

Those elements and activities that floods affect include roads, vehicles, and transport systems

in general. The impact on these systems leads to a cascading effect with possible local and/or

regional repercussions (Suárez et al., 2005).

Moreover, the effects of floods on cars and transport systems may worsen due to roads

themselves because a road network can modify the natural topography and create a new

drainage network, which can change the hydrological response of basins (Jones et al., 2000;

Wemple et al., 2001).

Floods are the main cause of disruption of public and private transport systems due to the

blockage of roads and the risk they generate for vehicles being driven or parked on floodplains

(Pregnolato et al., 2017, Teo et al. 2012a; Versini et al. 2010a). Vehicles can be washed away

by overflowing water bodies, effectively becoming debris that can cause additional damage by

impacting buildings and infrastructure and by clogging hydraulic structures (Teo et al. 2012b;

Kalantari et al. 2014; Arrighi et al. 2015; Pregnolato et al. 2017).

Vehicles are swept along during floods much more frequently than it seems, even in large

numbers in some cases. In 1989, a flood that took place in the city of Nagasaki, Japan, damaged

20,000 cars and 299 people died, of whom roughtly 20 died when their vehicles were dragged

away by overflowing flood water (Oshikawa and Komatsu, 2014). In August of 2004, a flash

flood affected the village of Boscastle in the United Kingdom, causing enormous damage and

sweeping away more than 100 vehicles, some of which blocked a bridge causing its collapse

while driving others to the sea (Teo et al. 2012a; Teo et al. 2012b). In May 2018 in Barranquilla

(Colombia), the torrents of water brought by a precipitation episode exceeding 80 mm swept

away more than 40 cars (El Tiempo, 2018). In September 2019, rainfall exceeding 400 mm in

48 hours fell in SE Spain. Seven people were killed, of whom four were trapped in their cars

and died (Levante, 2019). In Brazil, extremely heavy rainfall in January 2020 and at least 53

people died, and several people did so inside their vehicles (Fhola de S. Paulo, 2020).

Several studies have shown that the main cause of death in cities during flood events

corresponds to cars being swept away when they are driven by flooded roads (Jonkman and

Kelman 2005; Drobot et al. 2007; Fitzgerald et al. 2010; Kellar and Schmidlin 2012). In

developed countries a high percentage of these deaths occurs during flash floods when drivers

try to cross overflowing water bodies instead of avoiding them (Fitzgerald et al. 2010; Kellar

and Schmidlin 2012). Hence, in areas subject to flash floods almost half of the victims are

passengers trapped inside their own vehicles (Versini et al. 2010a). In the USA, 45.4% of

people who died during flooding had been inside vehicles (Jonkman & Kelman, 2005). In

Australia, 48.5% of deaths in floods are related to the use of motorized vehicles (Fitzgerald et

al., 2010). In Europe, approximately 13% of fatalities during floods occur inside vehicles

(Jonkman and Kelman, 2005). Every year in Texas (USA), an average of 15 drivers drown

when they drive their vehicles on flooded underground roads or through tunnels (Maples &

Tiefenbacher, 2009).


2

Among the parts of the roads that are affected by the rivers floods are the bridges, which are

very important infrastructure works. The failure of these structures has highly negative tangible

impacts, both direct and indirect, and intangible impacts such as loss of human life and

significant social and environmental problems.

A high percentage of bridge failures worldwide occur as a result of river floods. For example,

according to Wardhana and Hadipriono (2003), of the 503 bridges that collapsed in the United

States between 1989 and 2000, approximately 53% failed due to river floods; most of these

failures occurred within the service life of the bridges, whose ages ranged from 1 to 157 years,

averaging 52.5 years. Owing to the failure of these structures 76 people died and 161 others

were injured.

Colombia has a similar percentage of bridge failures due to floods: of the 63 failures reported

between 1986 and 2001, 47% were caused by floods, scour and avalanches (Muñoz, 2002). In

Taiwan several bridges have failed in recent years due to the effects of floods (Ko et al., 2014).

In addition, climate change is expected to increase the probability of bridge failure due to

erosion caused by floods (Khelifa et al, 2013).

Among the impacts generated by bridge failures is the traffic disruption, which can last a

considerable time if the damage to the infrastructure has been severe. Normally, this traffic

disruption affects the performance of many activities, generating a chain reaction that has

important social and economic consequences.

Apart from fatalities, damaged infrastructure and interrupted traffic, rescuing people trapped in

their vehicles in flooded areas demands costly investments in money and time terms (Smith et

al. 2017). Moreover, as a result of climate change and growing urban development, such threats

are expected to continue in the future (Dawson et al., 2016; Xia et al., 2011). Therefore, for an

adequate land management it is necessary to identify safe areas and the risk to which the

different vehicle types and bridges are exposed during floods.

However, despite the negative impact of floods, and the fact that the integral management of

such events requires assessing the risk posed for vehicles, very few studies have centred on

determining the negative effects of floods on transport systems (Suarez et al., 2005; Molarius

et al., 2014, Mitsakis et al., 2014). Very few studies have attempted to assess the stability of

partially submerged vehicles or to determine the risk to which vehicles are subjected or to

establish the risk of bridge failure due to flooding.

Due to this, in the present investigation a new methodology was developed to estimate the

impact that river floods can have on a road network, trying to cover several of the most affected

elements when this type of event occurs. Three different scenarios were considered:

(i) The risk of vehicle instability in the floodplains was determined. The proposed methodology

was applied in a case study in which an urban area was considered.

(ii) The risk of instability of vehicles in stream crossings, most of which are located in rural

areas, was established. The procedure developed was applied to stream crossings in a Spanish

municipality.

(iii) The risk of bridge failure due to flooding was evaluated. The proposed methodology was

implemented in 12 Spanish bridges of different characteristics.


3

In these three scenarios, procedures were developed that have a common methodology, which

is based on the integration of the flooding hazard and the vulnerability of the exposed elements.

According to the literature review carried out, currently there is no methodology available that

allows estimating risk with the approach proposed here or trying to cover as many scenarios as

those studied here.

1.2 Objectives

The general objective of this research is to develop a methodology to estimate at the regional

level the risk of vehicles and bridges instability due to flooding.

The specific objectives of the research are the following:

• Analyse the vehicle stability models during floods and select the most suitable for risk

determination.

• Develop a methodology to assess the risk of vehicle instability due to urban flooding

• Establish a methodology for determining the risk of vehicle instability in stream crossings.

• Define a methodology to determine the risk of bridge failure due to flooding.

1.3 Flood risk

Risk is defined as the combination of the probability of a flood occurring and its possible

negative consequences for human health, environment, cultural heritage, economic activity and

infrastructure (Ministry of the Presidency of Spain, 2010). These negatives consequences are

understood as the vulnerability of the receptors to such an event. Figure 1.1 presents a diagram

of the process that must be implemented to obtain the risk. According to this scheme, to

calculate the risk it is necessary to previously know the hazard, which is characterized by the

frequency of occurrence of the flood and by indicators of its magnitude or intensity, and the

vulnerability. This vulnerability is a function of exposure, which indicates the potential

receptors of the flood, and susceptibility, which indicates the level of damage the receptors may

suffer.

Figure 1.1 Diagram illustrating the process that must be implemented to calculate the risk

Frequency Magnitude

Hazard Vulnerability

Risk

Susceptibility Exposure


4

1.3.1 Flood hazard

Hazard is defined as the probability of occurrence of a potentially damaging flood event over a

certain period of time and at a given site. Floods, which are classified as natural hazards, are

physically characterized by indicators of their magnitude or intensity, such as depth, flow

velocity, and duration. The conversion of discharges to these variables is normally carried out

through hydrodynamic models, which range from one-dimensional stationary models to two-

dimensional non-stationary models. Usually, the main channel of the river is studied using one-

dimensional models, which do not require too much information and are not so expensive in

computational terms, and the floodplain is modelled two-dimensionally.

The probability of occurrence of floods is normally expressed by the frequency of occurrence

expressed as the return period or by the probability of non-exceedance. This probability is

normally calculated through statistical methods, which are based on recorded data.

1.3.2 Vulnerability

Vulnerability represents the characteristics of a system that describe its potential to be damaged

(Samuels et al., 2009; UNISDR, 2009). It is a function of the degree of exposure, which

indicates the potential receptors to the flood event, and the susceptibility, which indicates the

level of damage that these receptors may experience. According to Schanze (2006), the damage

generated by floods depends on the vulnerability of the exposed elements. The more elements

contains a system, the more vulnerable to flooding it will be. Likewise, the damages will be

more extensive as these elements at risk are more susceptible and more exposed (Scheuer et al.,

2011).

Susceptibility indicates the propensity of the exposed elements to damage (Samuels et al. 2009),

therefore it depends on the type of flood event and the constitution of the exposed elements

(Schanze, 2006). Susceptibility represents a measure of the potential negative consequences of

receptors according to their characteristics or social value, such as monetary value, human lives,

etc.

Susceptibility is usually expressed through damage or loss functions. The most used are the

depth - damage functions, which relate the depth of the flood with the damage that could be

generated in the elements at risk. In these functions, as the depth of the flood increases, the

damage generated in the exposed elements increases.

Exposure is a measure of potential receptors of the hazard and can be expressed in different

units, such as the number of potentially affected people or property. Generally, the

quantification of the exposed elements is carried out using geographic information systems,

which allow various types of analysis, including quantitative methods.

1.3.3 Calculation of risk

According to UNISDR (2009), risk (R) can be calculated by multiplying the probability of

occurrence (P) of an event by its consequences (C), as presented in Equation 1.1:

R = P * C [1.1]


5

By implementing equation 1.1 and plotting the probabilities of occurrence of flood events

against their corresponding consequences or damages, a graph similar to that presented in

Figure 1.2 is obtained.

Figure 1.2 Damage - probability curve

Source: Meyer et al. 2009

The area under the curve obtained by joining the calculated consequences for each probability

corresponds to the total damage, which can be represented through the following expression

presented by Hashimoto et al. (1982):

[1.2]

Where Risk (R) indicates the expected annual damage, V is the vulnerability expressed as the

probability of failure when the event of magnitude y occurs, Fy is the cumulative distribution

function of y and fy is the probability density function of the magnitude y.

1.4 Document structure

This document is made up of six chapters, in which the development and implementation of the

proposed methodology is described in detail. The first chapter corresponds to the introduction

and includes the motivation to carry out the research, its objectives and the description of the

components and the calculation of the risk.

Chapter two discusses the stability models of partially submerged vehicles developed in recent

years that can be applied to one or more types of vehicles according to their authors. The main

strengths and weaknesses of these models are presented and the most robust of them is selected.

Chapter three describes the established methodology to determine the risk of vehicle instability

in urban areas due to flooding. It is made a detailed description of the process that must be

followed to estimate the hazard, the vulnerability and the risk of vehicles, and of the

implementation of the methodology in a case study.

1/200 1/100 1/20 1/5

Exceedance probability

D4

D3

D2

D3

Dam

age

RTotal

𝑅 = ∫ 𝑉(𝑦) 𝑑𝐹𝑦

1

0

= ∫ 𝑉(𝑦) 𝑓𝑦(𝑦)𝑑𝑦∞

0


6

Chapter four presents the developed methodology to estimate the risk of vehicle instability at

stream crossings. The procedure that allows obtaining each of the risk components and the

application of the methodology in a case study are described.

Chapter five presents the developed methodology to determine the risk of bridge failure due to

flooding by analysing the integrity of the structure and the hydrological, hydraulic and

morphological characteristics of the water current and watershed.

Chapter six presents the main conclusions of the research carried out and proposes future lines

of research that will allow further progress in determining the risk of transport systems due to

river overflows.

Chapter 2, Review and analysis of vehicle stability models during floods .

7

2 REVIEW AND ANALYSIS OF VEHICLE STABILITY MODELS DURING

FLOODS

2.1 Introduction

Flood water can affect vehicles significantly, which in turn can increase the negative effects of

floods as vehicles are washed away by the flow and become a form of debris. (Teo et al. 2012a;

Versini et al. 2010a). In cities, most fatalities during floods occur inside vehicles (Fitzgerald et

al. 2010; Kellar and Schmidlin 2012). Additionally, as a result of urban growth and changes in

climate and meteorological conditions, the probability of urban floods continue presenting has

increased, so the risk of vehicles become unstable during these events is growing (Xia et al.,

2011; Shu et al., 2011).

Consequently, it is necessary to establish thresholds for vehicle stability during this type of

events to provide information necessary for flood risk management. However, despite the

danger caused by vehicles swept away and the fact that once vehicles have been washed away

they can aggravate flood impacts, very few studies have been carried out on this topic so far

(Suárez et al. 2005; Teo et al. 2012a; Arrighi et al. 2015).

Most of the available studies were conducted in laboratory flumes during the 60's and 70's while

some theoretical analyses were done in the 90's. However, given the significant changes

undergone by vehicles over the last decades, it is considered that these studies are not

representative of current conditions anymore (Arrighi et al. 2015; Teo et al. 2012a). A review

of the state of the art was presented by Martínez - Gomariz et al. (2016a). This chapter develops

an in-depth analysis of some of the methodologies presented in that study and includes the

methodologies developed over the last years.

This chapter discusses the existing models developed in recent years to establish stability

thresholds that can be applied to one or more types of vehicles according to their authors. In

order to do this, a description of these stability models is made first, grouping them according

to how they consider vehicle watertightness. Subsequently, the stability thresholds proposed by

these models are inter-compared, based on the type of cars for which they were developed.

Finally, the ranges in which these stability thresholds fluctuate are compared with the pairs of

velocity and depth data measured in laboratory for which the studied cars became unstable.

2.2 Description of the studied stability models

On a partially submerged vehicle, the forces of floating FB, lift FL, own weight W, drag FD and

friction FR act (Martínez–Gomariz et al., 2017). The action of all these forces gives way to three

hydrodynamic mechanisms coming into play, which can destabilize a vehicle: floating, sliding

and toppling. Loss of floating stability occurs when forces floating FB and lift FL exceed the

vehicle’s weight (W), causing for most cases the rear wheels to lose traction, due to weight

distribution in modern vehicles, making the vehicle rotate on its front wheels and in many cases

be washed away by the flow. This type of instability occurs mainly when the flow moves at a

slow velocity and high depths of water are found. Loss of sliding stability occurs when drag

force FD generated by flow exceeds friction force FR, which depends on the friction coefficient

between the vehicle’s tire rims and the wet surface. An interaction takes place between the

floating and sliding mechanisms because both forces lift FL and floating FB lower normal force

FN which, in turn, lowers friction force FR.


8

Destabilization owing to the vehicle toppling seems to occur only when the vehicles have

already been washed away by the flow or have floated and found irregular land (Shand et al.

2011). This mechanism has been poorly studied to date. None of the available stability models

to date has considered this type of instability.

In recent years, some research has been conducted with the objective of establishing a stability

threshold for modern vehicles through the study of the interaction between these vehicles and

the flow. This threshold is usually defined through expressions that relate water depth and flow

velocity. However, many of these studies differ in the way they approach the problem and in

the driving factors considered in their analysis. As a result, they have produced different models

for the determination of this stability threshold.

According to some authors (Teo et al. 2012a,b), assuming that vehicles are completely

watertight during floods is a highly idealized condition, which is why they consider the entry

of water into vehicles when trying to determine the stability threshold. However, most authors

consider that, due to improvements in modern vehicles in aspects such as sealing against dust,

it is legitimate to assume that vehicles are watertight during flood events. Some of them

determine the stability threshold using the total energy of the flow (Ausroads 2008; Kramer et

al. 2016) while others use the product of flow velocity and depth. Among the latter, some

models establish a maximum limit for depth and flow velocity (DIPNR 2005; Shand et al. 2011;

Smith et al. 2014) and others a maximum limit only for depth (Moore and Power 2002;

Martínez-Gomariz et al. 2017). Finally, some authors have developed models that enable the

calculation of vehicle stability either considering or disregarding its watertightness; i.e., one of

these models establishes the stability threshold by registering the combinations of flow velocity

and depth that generate stability loss (Toda et al. 2013), another compares the forces acting on

the vehicle (Oshikawa and Komatsu 2014) and the third uses the Froude number and a mobility

parameter (Arrighi et al 2015).

The different models available for evaluating stability of vehicles exposed to flooding are

described in more detail here below. A synthesis of the main characteristics of these stability

models is presented in Table 2.1.

2.2.1 Stability models that consider non-watertightness of vehicles during floods

In order to understand the impact of water level and flow velocity in the hydrodynamic

processes that cause stability loss of a vehicle during a flood event, Teo et al. (2012a) and Teo

et al. (2012b) presented in similar papers a series of experiments in a flume using physical

models of three different vehicle types: a Mini Cooper, a BMW M5 and a Mitsubishi Pajero.

They used scales 1:43 and 1:18, satisfying the principle of geometric similarity. Additionally,

these authors assumed the vehicles were not completely watertight. These experimental data

were also reported by Xia et al. (2011).

Teo et al. (2012a) and Teo et al. (2012b) extrapolated their results to the prototypes and

established the stability threshold from the combinations of water depth and flow velocity that

cause the movement of the vehicles. On the basis of the obtained results, a graph was developed

by relating depth with flow velocity, this graph enabled the definition of three zones: a stable

zone where the interaction of flow velocities and depths does not affect vehicle stability, a

transition zone and an unstable zone in which flow velocities and depths would cause the

vehicles to move by sliding (Figure 2.1a).


9

However, according to Froude number similarity, the weights of the different scale physical

models were not correctly scaled. Consequently, the validation carried out for the 1:18 scale

was not sufficiently accurate. Additionally, they considered water came inside the vehicle from

the very beginning of the experiment whereas it appears the entry of water into the prototypes

is likely to occur not as fast as it was assumed. Owing to all this, the results presented by this

model should be used with caution.

2.2.2 Stability models that consider vehicle watertightness during floods

From the analysis of the experimental results reported by Bonham and Hattersley (1967),

Gordon and Stone (1973) and Keller and Mitsch (1993), Moore and Power (2002) defined the

threshold of instability through a linear relationship between flow velocity and depth for

subcritical regime and through the multiplication of these two parameters for supercritical

regime, assigning to this product a value of 0.6 (Figure 2.1b). They established the separation

between these relationships at 1.81 m/s. It should be noted that this stability model was based

on experimental tests carried out with vehicles having very different characteristics from current

ones, so the results may not be entirely valid today.

The Department of Infrastructure, Planning and Natural Resources of the New South Wales

Government (DIPNR 2005) considers that vehicle instability is initially generated by buoyancy

and establishes a stability threshold through a linear relationship between flow depth and

velocity. This threshold includes maximum values of 2.0 m/s for the velocity and 0.3 m for the

depth (Figure 2.1b).

Mens et al. (2008) obtained the stability thresholds for a standard car, a van, an ambulance and

a fire truck applying the stability model proposed by Keller and Mitsch (1993), as shown in

Figure 2.1b. However, as already noted, the characteristics of vehicles have changed

significantly in recent years, so the model applied could not be valid at present.

Based on the analysis of the data reported by Bonham and Hattersley (1967), Gordon and Stone

(1973) and Keller and Mitsch (1993), Australian Rainfall and Runoff -AR&R- (Shand et al.

2011) proposed provisional stability criteria for vehicles at rest (Figure 2.1b). According to their

dimensions, weight and free distance to the ground, the cars were classified into large 4WD,

large passenger and small passengers (Sections 2.3 and 2.4 use this same classification) and it

was considered that the stability limit for each of these types of vehicle is reached when the

product of flow velocity with depth is equal to 0.3, 0.45 and 0.6, respectively. According to

buoyancy limits, maximum depths of 0.5 m were defined for large 4WD vehicles, 0.4 m for

large passenger vehicles and 0.3 m for small passenger vehicles. A maximum flow velocity of

3.0 m/s was established for all vehicles to ensure human safety when leaving the vehicles,

following the recommendation reported by Cox et al. (2010). According to the authors, these

criteria have a provisional character and must, therefore, be updated.

From results reported in literature, Smith et al. (2014) proposed a stability threshold for small

vehicles and another for all other types of vehicle, considering in both cases a maximum limit

of flow velocity of 2.0 m/s (Figure 2.1b). The other criteria for both small and other vehicles

coincide with the ones defined by the AR&R in 2011 (Shand et al. 2011) for small vehicles and

large 4WD vehicles, respectively.


10

Kramer et al. (2016) conducted several laboratory tests using a 1: 9.8 scale physical model of

a VW Golf III and a 1:13.1 scale physical model of an emergency rescue vehicle. The results

indicated that the different combinations of flow velocity and depth that define the stability

threshold of the analysed vehicles describe a curve similar in shape to the curve of constant

total energy head. These authors established that the safety criteria for the transit of vehicles on

flooded roads must consider technical restrictions of each vehicle, such as the height of the air

inlets or the tightness of the electrical devices, in addition to stability aspects. Consequently, a

stability threshold equal to the total energy of the water was defined, giving it a constant value

equivalent to the minimum wading depth, according to the vehicle under study: for emergency

rescue vehicles this value was established at 0.6 m and for passenger vehicles at 0.3 m. This

last criterion coincides with that proposed by Ausroads in 2008 (Figure 2.1b).

Concerning the instability drivers, Kramer et al. (2016) concluded that in floods in which the

Froude number of the flow is less than 0.5, stability is controlled by the flotation forces and

does not seem to depend on the orientation of the vehicle with respect to the flow. In contrast,

when Froude numbers are greater than 0.5, the sliding instability mechanism becomes more

dominant and the incidence angle of the flow has an important effect.

Finally, through tests carried out with a prototype of the VW Golf III car, Kramer et al. (2016)

concluded that it is reasonable to assume watertightness conditions in order to define safety

criteria for vehicles in urban environments.

Smith et al. (2017) conducted measurements on a 2006 Toyota Yaris Sedan and a 1998 Nissan

Patrol GRII on a full prototype scale in order to determine the force required to overcome the

friction force when the vehicles were submerged at different depths of water at rest.

Additionally, they conducted tests on a 1:18 scale physical model of a 2005 Toyota Yaris Hatch

with the objective of determining the equivalent hydrodynamic force required to reproduce the

instability conditions of the prototype vehicle. The test results showed average values of 0.76

for the friction coefficient between the floor and the tyres and values fluctuating between 1.2

and 2.0 for the drag coefficient, which is used to calculate the drag force. Stability thresholds

were defined as the product of flow velocity and depth, finding values close to 0.5 for the Toyota

Yaris and higher than 1.0 for the Nissan Patrol. However, considering that conditions in real

world can differ widely from the controlled conditions in the laboratory and that several

simplifications were made in the tests performed, Smith et al. concluded that the stability

thresholds proposed by AR&R (Shand et al. 2011) are appropriate (Figure 2.1b).

Martínez–Gomariz et al. (2017) proposed a model to determine the stability of any vehicle

exposed to flooding based on the analysis of the results of experimental tests. Measurements

were made with 12 car physical models using three different scales (1:14, 1:18 and 1:24). From

the results, these authors defined a stability function that allowed them to establish a constant

value of the product of flow velocity and depth. This function was found on the basis of the

depth from which the vehicle starts to float and a stability coefficient which is calculated from

the friction coefficient between the tyres and the road and the following characteristics of the

vehicle: weight, free distance to the ground and plan area (Figure 2.1b).

Through the implementation of the obtained stability function by Martínez-Gomariz et al.

(2017) and using friction coefficient values of 0.25 and 0.75, the model enables to obtain a

graph showing depth versus flow velocity for each vehicle. This graph shows a stable zone, a

transition zone and a zone in which vehicles would reach instability conditions. However, it

should be noted that in all tests performed, the friction coefficient fluctuated between 0.52 and


11

0.62, while for the calculation of the stability thresholds the values adopted were of 0.25 and

0.75, which are very far from the experimental range.

2.2.3 Stability models that consider watertightness and non-watertightness of vehicles during

floods

Oshikawa and Komatsu (2014) conducted experimental tests with 1:24 scale physical models

of a Nissan March compact car and a 4WD Toyota Land Cruiser. From the results analysis the

stability threshold was determined as the ratio between the drag force and the friction one. A

value of this ratio greater than 1.0 indicates that the vehicle would be washed away by the water

flow.

Values of drag and lift coefficients were experimentally determined and used to calculate the

corresponding forces exerted by the flow on the vehicle. The drag coefficients fluctuated

between 0.8 and 5.1 for the compact car, and between 2.1 and 3.6 for the 4WD car. Lift

coefficients varied between -0.28 and 0 for the compact vehicle and between -0.52 and -0.17

for the 4WD vehicle. In the cases where water can enter the vehicle, there will be a decrease in

the flotation force due to the vehicle porosity, which was defined with a minimum value of 0.0

when the vehicle was well-closed and with a maximum value of 0.5 that corresponded to the

cases where the dead weight of the vehicle and the buoyancy were balanced. Therefore, it is

possible to define a safe zone below the obtained stability threshold with a friction coefficient

of 0.4 and a porosity of 0.0, and a danger zone above the result for a friction coefficient of 0.6

and a porosity of 0.5 (Oshikawa and Komatsu 2014) (Figure 2.1c).

Using a similar approach to that of Oshikawa and Komatsu (2014), Toda et al. (2013)

performed laboratory tests using physical models at scale 1:10 of a sedan-style vehicle and 1:18

of a minivan. These authors obtained friction coefficients equal to 0.26 for the sedan vehicle

and 0.57 for the minivan with the car oriented in the flow direction and the handbrake on. With

the car oriented transversely to the flow and with the handbrake off, the coefficients of friction

were equal to 0.565 for the sedan vehicle and 0.65 for the minivan. Porosity values were

established as 0.2, 0.3 and 0.5. It was concluded that vehicles are likely to start moving with

depths greater than 0.5 m and velocities greater than 2.0 m/s.

According to Arrighi et al. (2015), vehicle stability can be determined from the Froude number

and a mobility parameter. This parameter is defined for water depths greater than the height of

the chassis and considers the shape and the submerged relative weight of the vehicle. Arrighi

et al. (2016a) improve the estimation of the mobility parameter when considering the incidence

angle of the flow with the vehicle. The mobility parameter was calculated for experimental data

reported by Xia et al. (2011), Shu et al. (2011) and Xia et al. (2014). The results were plotted

against the corresponding Froude numbers, obtaining a stability threshold which determines a

safe zone and a dangerous zone (Figure 2.1c). It should be noted that this model allows

considering the entry of water into the vehicle during the flooding, because it allows modifying

the density of the car, which is required to calculate the mobility parameter. Also, it is important

to note that a certain degree of uncertainty is associated to the stability threshold, because

Arrighi et al. used the data reported by Xia et al. (2011), which present the inaccuracies already

discussed in Subsection 2.2.1.


12

0,0

0,2

0,4

0,6

0,8

1,0

0,0 1,0 2,0 3,0 4,0 5,0

Dep

th (m

)

Velocity (m/s)

p=0.5, µ = 0.6

p=0, µ = 0.4

Danger Zone

Safe Zone

0,0

0,2

0,4

0,6

0,8

1,0

0,0 1,0 2,0 3,0 4,0 5,0

Dep

th (m

)

Velocity (m/s)

p=0.5, µ = 0.6

p=0, µ = 0.4

Danger Zone

Safe Zone

0

1

10

100

1.000

0 1 10

Mo

bilit

y P

aram

eter

θv

(m)

Froude Number Fr

ARRIGUI ET AL. (2016)

Generic Car

Safe Area

Dangerous Area

θvcr = θvcr (Fr2)

0,0

0,2

0,4

0,6

0,8

0,0 1,0 2,0 3,0 4,0 5,0

Dep

th (m

)

Velocity (m/s)

MENS ET AL. (2008)

Fire Engine Van

Ambulance Car

0,0

0,2

0,4

0,6

0,8

0,0 1,0 2,0 3,0 4,0 5,0

Dep

th (m

)

Velocity (m/s)

High Hazard

Low Hazard

Transition Area

0,0

0,2

0,4

0,6

0,8

0,0 1,0 2,0 3,0 4,0 5,0

Dep

th (m

)

Velocity (m/s)

High Hazard

Low Hazard

Transition Area

0,0

0,2

0,4

0,6

0,8

0,0 1,0 2,0 3,0 4,0 5,0

Dep

th (m

)

Velocity (m/s)

AR&R (2011)Small PassengerLarge PassengerLarge 4WD

0,0

0,2

0,4

0,6

0,8

0,0 1,0 2,0 3,0 4,0 5,0

Dep

th (m

)

Velocity (m/s)

SMITH ET AL. (2017)

Small Passenger

Large 4WD

0,0

0,2

0,4

0,6

0,8

0,0 1,0 2,0 3,0 4,0 5,0

Dep

th (m

)

Velocity (m/s)

SMITH ET AL. (2014)

Small Passenger

Other Types of Car

a.- Stability models that consider non-watertightness of vehicles

b.- Stability models that consider watertightness of vehicles

c.- Stability models that consider watertightness and non - watertightness of vehicles

Different scales have been used in panels a, b and c for better visibility

Figure 2.1 Stability thresholds for vehicles in flood events

KRAMER ET. AL (2016)

Passenger Cars

0,0

0,2

0,4

0,6

0,8

0,0 1,0 2,0 3,0 4,0 5,0

Dep

th (m

)

Velocity (m/s)

(v * H)upper, µ = 0.75

(v * H)lower, µ = 0.25

hb

KRAMER ET. AL (2016)

Emergency Cars

MARTINEZ-GOMARIZ ET AL. (2017)

Generic Car

Uncertainty Zone

Safety Zone

OSHIKAWA AND KOMATSU (2014)

4WD Cars

OSHIKAWA AND KOMATSU (2014)

Compact Cars

0,0

0,2

0,4

0,6

0,8

0,0 1,0 2,0 3,0 4,0 5,0

Dep

th (m

)

Velocity (m/s)

AUSROADS (2008)

No distiction of type of car

0,0

0,2

0,4

0,6

0,8

0,0 1,0 2,0 3,0 4,0 5,0

Dep

th (m

)

Velocity (m/s)

MOORE AND POWER (2002)


0,0

0,2

0,4

0,6

0,8

0,0 1,0 2,0 3,0 4,0 5,0

Dep

th

(m)

Velocity (m/s)

DIPNR (2005)


0,0

1,0

2,0

3,0

4,0

5,0

0,0 1,0 2,0 3,0 4,0 5,0 6,0 7,0 8,0

Dep

th (m

)

Velocity (m/s)

TEO ET AL. (2012)


Unstable

Hydraulic

Zone

Stable

Hydraulic

Zone


13

2.3 Comparison of vehicle stability thresholds

2.3.1 Assuming vehicle watertightness

Figure 2.2 compares the results obtained by applying the stability models that consider vehicle

watertightness to three different types of cars according to the classification proposed by the

AR&R (Shand et al. 2011): large 4WD, large passengers and small passengers. Although the

stability models of DIPNR (2005), Ausroads (2008) and Kramer et al. (2016) were proposed

for any type of vehicle, they are only shown in the graph for small passenger vehicles, because,

in reality, the vehicles they used fell within this category.

For the implementation of the stability models of Arrighi et al. (2016a) and Martínez-Gomariz

et al. (2017), the following vehicles were used: (i) large 4WD cars: Mercedes G55 AMG and

Audi Q7; (ii) large passenger cars: Mercedes GLA and Ford Focus; (iii) small passenger cars:

Mini Cooper and Toyota Yaris.

33

Figure 2.2 Comparison of vehicle stability thresholds during floods proposed by stability

models that consider car watertightness

The analysis of Figure 2.2 allows identifying how the studied stability models generate a wide

range of stability thresholds, which are based on the decision criteria established in each case.

For example, in the case of 4WD vehicles, with a flow velocity of 3.5 m/s, it can be observed

that the stability models proposed by AR&R (2011) and Smith et al. (2017) consider it is not

safe to drive with any depth, while the models proposed by Moore and Power (2012) and

Martínez-Gomariz et al. (2017) consider safe to drive with depths approximately equal to or

less than 0.18 meters and Oshikawa and Komatsu (2014) establish this depth limit at

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5 5,0

Dep

th (m

)

Velocity (m/s)

Large 4WD vehicles

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5 5,0

Dep

th (

m)

Velocity (m/s)

Large passenger vehicles

0,00

0,05

0,10

0,15

0,20

0,25

0,30

0,35

0,40

0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5 5,0

Dep

th (

m)

Velocity (m/s)

General and small passenger vehicles Moore and Power, 2002 DPINR, 2005 Ausroads, 2008 – Kramer et al., 2016 AR&R, 2011 – Smith et al., 2017 (4WD and small cars) Oshikawa and Komatsu, 2014

Vehicle

Type of

vehicle

Stability model

Arrighi et al.

(2016)

Martínez–Gomariz

et al. (2017)

Mercedes G55 AMG 4WD

Mercedes GLA Large Pass.

Mini Cooper Small Pass.

Audi Q7 4WD

Ford Focus Large Pass.

Totota Yaris Small Pass.


14

approximately 0.45 meters. Variations of similar order of magnitude are observed for large and

small passenger vehicles.

There are also differences in the shape of the safety thresholds provided by the different stability

models, presenting different decreases in depth as flow velocity increases (Figure 2.2).

Concerning high velocities, on the one hand, Arrighi et al. (2016a) do not establish a limit to

flow velocity for the circulation of vehicles with depths lower than the chassis height. On the

other hand, the stability models proposed by Martínez-Gomariz et al. (2017) and Moore and

Power (2002) admit limits to flow velocity for low flow depths. The remaining models establish

maximum velocities values between 3.0 m/s and 5.0 m/s to define the stability threshold.

From Figure 2.2, it can be underlined that the stability thresholds proposed by Moore and Power

(2002) for velocities greater than 1.81 m/s, AR&R (2011), Martínez-Gomariz et al. (2017) and

Smith et al. (2017) for large 4WD vehicles are equal or quite similar to each other. The same

similarity is observed among the stability models proposed by DIPNR (2005), Ausroads (2008)

and Kramer et al. (2016), but for a different range of values.

2.3.2 Assuming vehicle non-watertightness

Figure 2.3 compares the results obtained when implementing the stability models that consider

non-watertightness of the vehicles. Considering that the model proposed by Teo et al. (2012)

establishes an instantaneous water entry into the vehicle, and in order to obtain comparable

figures, this graph presents the values proposed by Oshikawa and Komatsu (2014) for an 4WD

vehicle with porosity equal to 0.5 and the results obtained by Arrighi et al. (2016a) to a

Mercedes G55 AMG car, which corresponds to a large 4WD vehicle. In the latter case, three

scenarios were considered with different amounts of water entering the vehicle, increasing the

weight of the car by 250, 300 and 400%. The increase in weight equal to 250% is approximately

the same as the average increase considered in the experimental data of the 4WD car used by

Teo et al. (2012).

Note: The stability model of Arrighi et al. (2016a) was applied for a Mercedes G55 AMG car considering that the

water volume getting inside the vehicle increases its density by a 250, 300 and 400%

Figure 2.3 Comparison of vehicle stability thresholds during floods proposed by models that

consider large 4WD vehicles and car non-watertightness

0,0

1,0

2,0

3,0

4,0

5,0

0,0 1,0 2,0 3,0 4,0 5,0 6,0 7,0 8,0

Dep

th (m

)

Velocity (m/s)

Car density * 2.5 Car density * 3.0

Car density * 4.0

Teo et al. (2012) Oshikawa and Komatsu, 2014

Arrighi et al. (2016). Car: Mercedes G55 AMG


15

The information shown in Figure 2.3 makes it possible to conclude that for low velocities the

stability model proposed by Teo et al. (2012) establishes a stability threshold through the

combination of flow velocities and depths that are considered unsafe or exceed several times

the limit values proposed by the other stability models. In general, the stability thresholds

proposed by Arrighi et al. (2016a) for a weight increase of 300% and Oshikawa and Komatsu

(2014) are quite similar to each other. For high velocities, Teo et al. (2012) consider that speeds

higher than 6.8 m/s are unsafe with any depth, while Arrighi et al. (2016a) do not set limits for

low depths. The model proposed by Oshikawa and Komatsu (2014) only consider flow

velocities lower than 5.0.

2.4 Comparison of vehicle stability thresholds with experimental data

The goal of this sub-section is to compare experimentally obtained data of depth and flow

velocity in which the vehicles studied under watertight conditions lost their stability with the

ranges of values in which the thresholds of the previous stability models fluctuate for the three

types of vehicles defined by the AR&R in 2011 (Figure 2.4). In the determination of these

ranges, the stability model of Moore and Power (2002) was not considered because they used

experimental and analytical data for old cars, which had different characteristics from modern

ones.

2.4.1 Experimental data

The results for experimental data are condensed in Figure 2.4 as dots. In general, it is observed

in all cases that, as expected, the depths found experimentally show a tendency to decrease as

flow velocity increases. However, this tendency seems to differ between data obtained in

different laboratory tests, since the decrease in depths related to the increase in velocities is

bigger in some measurements than in others. For example, in the data measured for large

vehicles 4WD by Smith et al. in 2017, there is a much more pronounced decrease in the depths

causing vehicle destabilization than the decrease observed in the data recorded by Shu et al. in

2011. In other cases, the depths descend rapidly until a certain velocity is reached and from that

point onwards, this decrease is less pronounced (measurements made by Martínez-Gomariz et

al. in 2016 for large passenger vehicles), which contrasts with other measurements in which the

decrease in depths seems to have a more uniform tendency for the range of studied velocities

(for example, measurements made by Shu et al in 2011 for large passenger vehicles).

Figure 2.4 also shows that experimental data have a relatively high sample dispersion. For

example, Martínez-Gomariz et al. (2017) found that the Mercedes GLA reached conditions of

instability with a flow velocity of 1.98 m /s and a depth of 0.30 m, while in the study carried

out by Shu et al. (2011) it was found that the Ford Focus vehicle, which can be classified in the

same category that the Mercedes GLA but it should be less stable, lost its stability at the same

depth when the velocity reached a value of 4.0 m/s, that is, at twice the velocity found for the

Mercedes GLA.

The sample dispersion found in the trends followed by the consulted experimental data could

be due, in part, to the differences in the flow conditions of the flumes and the quality and scales

of the physical models used in the tests carried out. The used flumes width varied between 0.6

and 1.2 m, which implies that the sidewalls could have exerted an effect not considered in the

results in the case of the narrower ones. This is due to the fact that, when cars were oriented in

the normal direction to the flow, the walls could have been too close to the front and rear car

ends, affecting their behaviour. Additionally, the flume bottoms were constituted by different


16

materials among which are acrylic, bakelite, cement and plastic; due to this, the friction

coefficient between the car wheels and the bottom of the flumes fluctuated in relatively wide

range (Table 2.1), which generates variations in the stability thresholds.

Figure 2.4 Comparison of proposed stability thresholds for vehicles under watertight

conditions during floods with experimental data

On the other hand, scale models of different qualities have been used, such as: commercial

plastic models, model produced by powder-based laser sintering, radio control models and

diecast models. Not all of these models made an appropriate scaling of the geometric

characteristics and the weight of the prototype vehicles, which could be one of the causes of the

dispersion presented by the experimental results. In addition, the scales of the physical models

used fluctuated between 1:9.8 and 1:24 (Table 2.1), which represents a relatively wide range

and could generate important differences in the uncompensated scale effects that occur when

working with this type of models.

In all cases, the depths measured in the laboratory that generated vehicle stability loss were

greater than the free height between the floor and the chassis. This could suggest that, as

considered by the stability model proposed by Arrighi et al. (2016a), water depths lower than

chassis height would not destabilize the vehicles within the studied velocity range, which

corresponds approximately to the expected range in real situations.

2.4.2 Comparison between experimental data and stability models

For low flow velocities most of the stability models (grey area) seem to be too conservative, as

the proposed thresholds are relatively far from the experimental measurements (Figure 2.4).

Experimental Data

Author

Type of vehicle

Large 4WD Large passenger Small

passenger

Shu et al. (2011) Volvo XC90 Ford Transit

Ford Focus

Toda et al. (2013) Minivan Sedan

Xia et al. (2013) Audi Q7 Honda Accord

Martínez– Gomariz et

al. (2017) Mercedes G55 AMG Mercedes GLA Mini Cooper

Kramer et al. (2016) VW Golf III

Smith et al. (2017) Nissan Pat. GRII Toyota Yaris

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5 5,0 5,5 6,0

Niv

el

de

Ag

ua

(m

)

Velocidad (m/s)

VEHICULOS DE PASAJEROS PEQUEÑOS

Arrig ui et a l. (2016)

Kramer et al .

Range in which the proposed stability thresholds fluctuate

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5 5,0

Dep

th (

m)

Velocity (m/s)

Small passenger vehicles

0

0,1

0,2

0,3

0,4

0,5

0,6

0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5 5,0 5,5 6,0 6,5

Dep

th (

m)

Velocity (m/s)

Large passenger vehicles

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5 5,0 5,5 6,0 6,5

Dep

th (

m)

Velocity (m/s)

Large 4WD vehicles


17

For medium and high velocities, some of the experimental results start to fall within the range

of the proposed stability thresholds, especially for small cars. This situation could suggest that

some of the studied stability models, such as those of Oshikawa and Komatsu (2014) and Moore

and Power (2012) for large and small passenger cars (as can be seen in previous Figure 2.3),

propose combinations of flow velocity and depth that would not guarantee vehicle stability

during flood events. For high velocities some of the stability models seem too conservative. For

example, for reasons of passenger safety when leaving vehicles, the model of the AR&R (2011)

considers it unsafe to circulate at any depth when the velocities are higher than 3.0 m/s (Not

represented in Figure 2.4) and the model of Martínez-Gomariz et al. (2017) admits stable depths

that can be considered too low when compared with the experimental ones.

On the other hand, the stability models proposed by DIPNR (2005), Austroads (2008) and

Kramer et al. (2016) (Figure 2.1b) seem to be somewhat conservative for large passenger cars

and very conservative for 4WD vehicles, since the data found experimentally (Figure 2.4) are

quite different from the stability thresholds proposed by these models. In the case of the stability

model proposed by Kramer et al. (2016), this could be due to the fact that the stability threshold

was determined from the analysis of experimental results obtained for one single small

passenger vehicle.

2.5 Final Remarks

The available stability models have made simplifications that could affect the results achieved.

Some of the main simplifications are the following:

Only cars at rest have been considered.

Most of the experiments have been carried out on a horizontal surface.

The friction coefficient between the tyres and the road has not been studied in depth,

especially when considering it can vary during flood events.

The actual weight distribution of the vehicles (with greater weight in the front part due to

the location of the engine) has not been considered in several of the developed studies.

The tests have been conducted using a controlled flow. This is not representative of real-

life flow conditions, which could be, for example, variable or pulsating.

Measurements have been made in laboratory flumes, whose characteristics can vary

significantly from the conditions of the actual roads.

Most of the experimental studies have been carried out with scale physical models,

implying that some forces acting on the vehicles may not have been well represented due

to scale effects.

With the exception of the study developed by Martínez-Gomariz et al. (2017), experimental

tests have made measurements on very few cars, which were not always the most

vulnerable ones to flooding for each vehicle category.

Some of these simplifications are too restrictive so the experimental tests performed could have

produced results that are not sufficiently representative of the stability of vehicles against

floods.

With regard to the theoretical approach of the studied stability models, it should be noted that

the model developed by Arrighi et al. (2016a) combines several aspects that can make it one of

the most robust. Among these aspects, it is worth highlighting that the equations proposed are

based on a solid theoretical base and that include the use of Froude number, which is a very

important and widely used parameter in many formulations. In addition, this methodology


18

allows to consider simultaneously watertightness and non-watertightness conditions of the

vehicles and enables the calculation of a stability threshold for any vehicle considering key

factors as ground clearance and car density. Due to these reasons, in this methodology the

model developed by Arrighi was chosen to determine the stability of vehicles during floods.

Table 2.1 Studied models for the determination of vehicle stability

Water-

tightness of

vehicles

Author Year Used data

Scale

physical

models

Velo-

city

(m/s)

Depth

(m)

Froude

Number

Friction

Coeffic.

µ

Drag.

Coeffic.

Angle of

flow

β(1)

Stability Equation (2)

Non-water-

tightness Teo et al. 2012

Measurements on Mini Cooper, BMW M5, Mitsubishi

Pajero

1:43

1:18

2.37-

7.94

0.65 -

4.82

0.50 –

3.16 - - 90º - 180º Linear relationship between H and V

Water-

tightness

Moore and

Power 2002

Measurements reported by Bonham and Hettersley (1967),

Gordon and Stone (1973) and Keller and Mitsch (1993)(3)

1:16

1:25

0.48 –

3.69

0.025 –

0.57 - 0.3 -1.0 - 0º, 90º

H≤ (0,4-0,0376V) for V≤ 1,81

H*V≤ 0,6 for V> 1,81

DIPNR 2005 Analysis of laboratory tests not specified - - - - - - - V < -11*H + 3,3 V ≤ 2,0

AR&R 2011 Measurements reported by Bonham and Hettersley (1967),

Gordon and Stone (1973) and Keller and Mitsch (1993)(3)

1:16

1:25

0.48 –

3.69

0.025 –

0.57 -

0.3 -

1.0 - 0º, 90º

Small cars: H*V≤ 0,3 H ≤ 0,3 V ≤ 3,0

Large cars: H*V≤0,45 H ≤ 0,4 V ≤ 3,0

4WD cars: H*V≤ 0,6 H ≤ 0,5 V ≤ 3,0

Smith et al. 2014 Analysis of stability thresholds reported by AR&R in 2011

for vehicles and in 2010 for people - - - - - - -

Small cars: H*V≤ 0,3 H ≤ 0,3 V ≤ 2,0

Others cars: H*V≤0,6 H ≤ 0,5 V ≤ 2,0

Kramer et al. 2016 Measurements made on a VW Golf III and a LF 10/6

1:1

1:9.8

1:13.1

0 –

3.2

0 –

0.73 0 – 1.5 0.3 -

0º, 45º,

90º

Passengers cars: H+V²/2g ≤ 0,3

Emergency cars: H+V²/2g ≤ 0,6

Smith et al. 2017 Measurements on a Toyota Yaris 2005 and 2006 and a

Nissan Patrol 1998

1:1

1:18

0.80 –

6.56

0 -

0.828

0.30–

6.63

0.75 -

0.78

0.98 –

2.02 90º

Small cars: H*V≤ 0,3 H ≤ 0,3 V ≤ 3,0

4WD cars: H*V≤ 0,6 H ≤ 0,5 V ≤ 3,0

Martínez-

Gomariz et

al.

2017

Measurements made on BMW 650, Mini Cooper, BMW

i3, Mercedes GLA, Mercedes Class C, Range Rover

Evoque, Porsche Cayenne Turbo, Bentley Continental GT,

Volkswagen Touareg, BMW X6, Audi Q7, Mercedes G55

AMG

1:14

1:18

1:24

0.89 –

5.12

0.16 –

0.63

- 0.25 –

0.75 -

All

orientations

were

considered

𝐻 ∗ 𝑉 = 0,0158 ∗𝐺𝑐 ∗ 𝑀𝑐

𝑃𝐴∗ 𝜇 + 0,32

𝐻 < ℎ𝑏 =𝑀𝑐

𝜌 ∗ 𝐿 ∗ 𝑙 + 𝐺𝑐

Water-

tightness/

Non- Water-

tightness

Toda et al. 2013 Measurements made with a sedan-type vehicle and a

minivan (ambulance)

1:10

1:18

1.05 –

2.00

0.30 –

1.21 -

0.26 –

0.65

0.40 –

3.50

0º, 45º,

90º V ≤ 2,0 and H ≤ 0,5

Oshikawa

and Komatsu 2014

Measurements made on a Nissan March and a Toyota

Land Cruiser 1:24

1.47 –

7.35

0.24 –

1.08

0.90 -

2.77

0.40 –

0.60

0.75 –

5.1 90º Non-linear relationship between H and V

Arrighi et al. 2016 Measurements reported by Shu et al. (2011), Xia et al.

(2011) and Xia et al. (2014)

1:14

1:18

1:43

0.18 –

7.94

0.11 –

4.82

0.50 –

3.16 (4)

0.25 –

0.75 -

0º, 90º,

180º

0 ≤ 𝜃𝑉𝑐𝑟 𝜃𝑉 < 1⁄

𝜃𝑉𝑐𝑟 = 8,2 ∗ 𝐹𝑟2 − 14,1 ∗ 𝐹𝑟 + 5,4

𝜃𝑣 =2𝐿

(𝐻𝑣 − ℎ𝑐)∗

𝑙

𝑙 ∗ 𝐶𝑜𝑠𝛽 + 𝐿 ∗ 𝑠𝑖𝑛𝛽

∗ (𝜌𝑐 ∗ (𝐻𝑣 − ℎ𝑐)

𝜌 ∗ (𝐻 − ℎ𝑐)− 1)

(1) β = angle of incidence of the flow with respect to the vehicle: 0º = Vehicle oriented in the direction of flow and with the front facing the flow; 90º = Vehicle oriented in the direction perpendicular

to the flow; 180º = Vehicle oriented in the direction of flow and with the rear facing the flow

(2) H = Depth (m) V = Flow velocity (m/s) Gc = Ground clearance (m) Mc = Weight (kg) PA = Plan Area (m²)

µ = Friction Coefficient ρ = Water density (kg/m³) L = Length of the vehicle (m) l = Width of the vehicle (m) θvcr = Critical threshold

θv = Mobility parameter Fr = Froude Number Hv = Height of the vehicle (m) hc = Height of the planform (m) ρc = Car density (kg/m³) (3) These measurements were made in scale models of vehicle Ford Falcon, Morris Mini sedan, Toyota Corolla, Suzuki Swift, Ford Laser, Honda Civic and Ford LTD (4) Only reported by Xia (2011)

Chapter 3, Assessing the risk of vehicle instability due to flooding

21

3. ASSESSING THE RISK OF VEHICLE INSTABILITY DUE TO FLOODING

3.1 Introduction

When rivers overflow, transport systems can be badly affected as traffic is interrupted,

given the instability risk for those vehicles driving around or parked on floodplains (Teo

et al., 2012). Most published studies about this vehicles instability risk have focused on

determining the hazard or vulnerability of roads due to floods using the characteristics of

basins and road networks. Some include the method of flood hazard maps proposed by

Kalantari et al. (2014). This method allows the probability of flood hazards to be

calculated by a multiple factor analysis, which considers topography, land use, soil

texture and roadway density. Michielsen et al. (2016) proposed a methodology for

identifying vulnerability caused by the flooding of a transport network based on the

analysis of basin characteristics using statistical methods. Versini et al. (2010) presented

a method to evaluate the susceptibility of roads being flooded using geographic

information and statistical analysis methods based on general discriminant analysis

principles.

Of the few studies that have attempted to really assess the flooding risk, we found the

method set forward by Yin et al. (2016) to establish the risk of flash-floods on an urban

roadway network. In this methodology, risk is determined through the integral of the

multiplication of flood occurrence probabilities and their corresponding consequences,

established with the combination of flooded road length and the time during which roads

remain flooded. Pregnolato et al. (2017) developed a method to determine the impact of

flooding on a transport network by means of a function relating flood depth to interrupted

traffic. This study establishes the interruption risk by means of the integral of the result

of each rain event probability, multiplied by the expected interruption of traffic.

This chapter presents a methodology that determines the vehicle instability risk in urban

areas as a result of overflowing rivers with a formal statistical basis that allows the number

of at-risk vehicles per year to be determined. Bearing this objective in mind, the

mechanisms that cause a submerged vehicle to lose its stability are initially described. It

then goes on to describe the methodology followed by indicating the process to be used

to calculate hazard, vulnerability and the vehicle instability risk. Finally, it also presents

how this methodology is implemented to determine the vehicle instability risk in the

flood-prone areas of the towns of Massanassa and Alfafar, which lie south of Valencia

(Spain) and very close to the Spanish Mediterranean coastline.

3.2 Vehicle stability in flooded areas

To calculate vehicle instability conditions, a criterion needs to be defined to establish

when the depth and velocity of flows corresponding to different return periods floods

generate vehicle instability, which also depends on the characteristics of each vehicle

type.

As already noted in the previous chapter, some models have been recently developed to

determine vehicle stability during floods based on the vehicle-flow interaction analysis


22

(e.g., Teo et al., 2012; Austroads et al., 2008; etc.). A compilation and analysis of the

presently available methodologies were presented by Bocanegra et al. (2020). Of these

methodologies, the present study selected the model proposed by Arrighi et al. (2016) as

it is considered one of the most robust methodologies of those proposed.

From the horizontal forces balance acting on car i located on a plane at a slope of zero,

and based on the diagram provided in Figure 3.1, Arrighi et al. (2016) defined the

following mobility parameter θvi:

[3.1]

where ρc is the car’s mean density, ρ is water density, hc is the distance between the

chassis and the ground, H is the undisturbed water depth, β is the angle of flow incidence,

and Hv, L and l are car height, car length and car width, respectively.

Figure 3.1 Geometry of the car used to determine mobility parameter θv.

Source: Arrighi et al. (2016)

Mobility parameter θvi is defined for water depths greater than the chassis and is made up

of three factors: the first factor (2L/(Hv - hc)) takes account of the car’s shape; the second

considers the angle of flow incidence; the third factor contemplates the submerged weight

in relation to the car.

Mobility parameter θvi was calculated by Arrighi et al. (2016) with the experimental data

reported by Shu et al. (2011) and Xia et al. (2011, 2014), which included several measures

taken in seven car models on scales 1:14, 1:18 and 1:43 (Figure 3.2). The obtained results

allowed critical mobility parameter θvcr to be obtained, which can be established by the

equation below:

[3.2]

where Fr is the Froude number, which requires data only about water depth H and

velocity U. So a vehicle instability index, Si, can be defined as the relation between critical

mobility parameter θvcr defined in Equation 3.2 and mobility parameter θv for this vehicle

defined by Equation 3.1:

[3.3]

𝑆𝑖 =𝜃𝑉𝑐𝑟

𝜃𝑉𝑖

𝜃𝑉𝑐𝑟 = 8.2 𝐹𝑟2 − 14.1 𝐹𝑟 + 5.4

𝜃𝑣𝑖=

2𝐿

(𝐻𝑣 − ℎ𝑐)∗

𝑙

𝑙 ∗ 𝐶𝑜𝑠𝛽 + 𝐿 ∗ 𝑠𝑖𝑛𝛽∗ (

𝜌𝑐 ∗ (𝐻𝑣 − ℎ𝑐)

𝜌 ∗ (𝐻 − ℎ𝑐)− 1)


23

The interesting point about this index is that the different vehicle stability or instability

situations can be found depending on the value that it takes: if Si ≥ 1, then the vehicle will

destabilize due to sliding; if Si < 0, the vehicle will float; if 0 ≤ Si < 1, the vehicle will

remain stable.

Figure 3.2 Diagram of the mobility parameter θv vs Froude number.

Source: Arrighi et al.

3.3 Methodology to estimate the vehicle instability risk using formal statistics

The vehicle instability risk from flooding is determined by integrating the probability of

the vehicle being dragged or it floating (hazard) and the types and density of vehicles

located in flood-prone areas (vulnerability) at a given point of the territory (exposure). In

this methodology, instability risk, R, at a specific point is defined as the mean number of

vehicles that would destabilize annually per unit area. According to the Equation 1.2, this

risk can be calculated at a given point on the territory by employing the following

statistical integral adapted to this problem:

[3.4]

where V(si) is vulnerability, calculated by combining the damage function and exposure

to an event of magnitude Si; FSi is the accumulated distribution function of Si; fSi is the

density function of probability. The following subsections describe the procedure that

must be set up to calculate the risk and all its components.

𝑅 = ∫ 𝑉(𝑠𝑖) 𝑑𝐹𝑠𝑖

1

0

= ∫ 𝑉(𝑠𝑖) 𝑓𝑠𝑖(𝑠𝑖)𝑑𝑠𝑖

∞

0

3


24

3.3.1 Vehicle instability hazard

To calculate the vehicle instability hazard, information is required about the flooding

hazard (intensity of floods corresponding to different return periods), along with vehicles’

physical characteristics. The stream intensity is usually established with maximum flow

water depth and its corresponding velocity. A similar graph to that in panel A of Figure

3.3 was obtained when graphically representing the occurrence of each flood event

against its intensity.

The hazard flood is normally represented on maps with its maximum water depth h and

its velocity u for different return periods. With the information depicted on these maps,

instability index Si is calculated for every vehicle i on each point of the territory using

Equation 3.3. When graphically representing the intensity of each flood event against its

corresponding Si, a similar graph to that shown in panel B of Figure 3.3 is obtained.

Finally, the graphical representation of the exceedance probability of all flood events

against their corresponding Si provides a similar figure to that seen in panel C in Figure

3.3, which depicts the vehicle instability hazard. In other words, the vehicle instability

hazard can be represented on vehicle instability index Si maps for each return period.

Figure 3.3 Diagram illustrating the process that must be implemented to calculate the

instability hazard in one vehicle i


A. B.

0

1

0 1

Exceedence probability

Flo

od I

nte

nsity

(h,

u)

Vehicle instability index Si

Vehic

le insta

bili

ty in

dex S

i

Flo

od I

nte

nsity

(h,

u)


Instability Stabi-

lity Instability

C.


25

3.3.2 Vulnerability

Vulnerability represents the characteristics of a system that describes its damage potential

(Messner and Meyer, 2006; Samuels et al., 2009; UNISDR, 2009), which is calculated

by combining exposure and susceptibility. Exposure for one vehicle type i is calculated

by multiplying vehicle density d at a point of interest by the proportion gi of this type of

vehicle in a vehicles fleet in the study area. In order to calculate the flood susceptibility

of one vehicle i at a given point, damage function D(si) must be established using vehicle

instability index Si. The present methodology assumes that damage is directly associated

with vehicle stability, and in such a way that when it is unstable, i.e., when vehicle

instability index Si calculated using Equation 3.3 takes negative values, or values

equalling or exceeding 1, the damage function takes a value of 1, which means that 100%

damage has taken place. When the vehicle remains stable, i.e. when the instability index

takes positive values below 1, the damage function takes a value of 0, which means that

the vehicle is not damaged. In mathematical terms, the damage function is defined as

follows:

𝐷(𝑆𝑖) =

Finally, the vulnerability V(Si) of one vehicle i at a given point of interest is calculated by

this equation:

[3.6]

3.3.3 Vehicle Instability Risk

The instability risk is determined by Equation 3.4. When substituting Equation 3.6 in

Equation 3.4, and bearing in mind the different vehicle types, the following expression is

obtained:

[3.7]

where K corresponds to the number of vehicle types by means of which the whole fleet

is represented.

Figure 3.4 presents a diagram of the procedure that must be followed to calculate the

instability risk of a vehicle type i at a point on the territory. Panel A corresponds to the

instability hazard, which is calculated as described in Figure 3.3. Panel B presents the

damage function, which is calculated as indicated in Equation 3.5. When the instability

hazard is combined with damage function D(si), each probability of a flood event

happening takes a certain damage function value. When graphically representing the

probability of each flood event against the corresponding damage function values, a

similar graph to that found in panel C is obtained, and the instability risk for a vehicle

type i at a point on the territory corresponds to the area under this curve.

𝑅 = ∑ 𝑑 𝑔𝑖

𝐾

𝑖=1

∫ 𝐷(𝑠𝑖) 𝑑𝐹𝑆𝑖

1

0

= ∑ 𝑑 𝑔𝑖

𝐾

𝑖=1

∫ 𝐷(𝑠𝑖)𝑓𝑆𝑖(𝑠)𝑑𝑠

∞

0

0 if 0 ≤ Si < 1, (Stable vehicle)

1 otherwise (Unstable vehicle) [3.5]

𝑉(𝑠𝑖) = 𝑑 𝑔𝑖 𝐷(𝑠𝑖)


26

Figure 3.4 Diagram of the instability risk of a single vehicle type i

As previously mentioned, vehicle instability hazard is represented on vehicle instability

index Si maps and each Si has a corresponding damage function D(si) value. Considering

this, the value of this function between two flood events with return periods Tj and Tj-1,

respectively, is obtained by defining a new function known as D(Si,j), which is calculated

by averaging the damage function D(Si) values corresponding to the two superior and

inferior events in terms of T. Taking into account this, the following expression is

obtained when discretely solving Equation 3.7:

[3.8]

where j corresponds to the flood hazard map for return period Tj and Tmin corresponds to

the shortest return period from which flooding commenced.

The concept of Tmin is introduced into Equation 3.8. Seeing that flood events with a

relatively low return period have a much stronger effect on the final risk values than the

less frequent events, determining the value of the return period Tmin is particularly

important because any mistakes or inaccuracies in this value might involve over- or

underestimating the risk. The impact of Tmin on the risk values is illustrated in the

sensitivity analysis of the case study in the next section (Subsection 3.4.7).

0

1

Damage function D(si)

Vehic

le insta

bili

ty in

dex S

i

1 0

A. B.

0

1


Risk

1/Tmin

Stability

Instability

Instability

C.


Dam

age f

unctio

n D

(Si)

0

1

Vehic

le insta

bili

ty in

dex S

i


𝑅 = ∑ 𝑑 𝑔𝑖 ∑ 𝐷(𝑠𝑖,𝑗) (1

𝑇𝑗−1−

1

𝑇𝑗)

𝑁

𝑗=𝑇𝑚𝑖𝑛

𝐾

𝑖=1


27

3.4 Applying a case study

In order to verify the procedure’s applicability to a real case, to analyze the validity of the

obtained results and to determine their sensitivity to Tmin, the developed methodology was

implemented to establish the vehicle instability risk in the Spanish towns of Massanassa

and Alfafar, which are located in the flood extent of Rambla del Poyo.

3.4.1 Description of the study area

La Rambla del Poyo is an intermittent watercourse located in the province of Valencia

(east Spain). It flows into the coastal L´Albufera lagoon, and its water basin covers 430

km² (Figure 3.5). This basin is classified as a Mediterranean basin with a semiarid climate,

mean annual rainfall of 450-500 mm, intense autumn and spring rainfall, and low winter

and summer rainfall values. The basin’s slope ranges between values over 16% in the

high part and below 2% in the low part. The configuration of the network of riverbeds

favours the rapid concentration of flows at the head, followed by retarded flows in the

main watercourse. The ravine is characterized by flash floods with very marked

hydrogram peaks and short baseline times (Salazar et al., 2012).

Figure 3.5 Location of the Rambla del Poyo basin and the study area

Some of the towns affected by flooding are located halfway and in low parts of the basin.

They include the towns of Massanassa and Alfafar, which lie in the lower basin part where

less pronounced slopes predominate. In these towns, land use is residential. Shops and

services occupy ground floors, especially in the areas close to their town squares.

3.4.2 Characterization and exposure of the vehicles in the study area

The way the vehicles are distributed in the study area was established with the data

published in 2018 by the Spanish Association of Manufacturers of Automobiles and

Lorries (ANFAC, 2018):


28

1. Smaller cars, with 26% of the total. This vehicle type was represented by the car

model Seat Ibiza.

2. Compact vehicles, with 32% of the total. This vehicle type was represented by the

car model Seat León.

3. Small SUVs, with 15% of the total. This vehicle type was represented by the car

model Peugeot 2008.

4. Medium-sized SUVs and larger vehicles, with 27% of the total. This vehicle type

was represented by the car model Volkswagen Tiguan.

Table 3.1 presents the main characteristics of these vehicles.

According to Francés et al. (2008), and by considering both parked vehicles and moving

traffic, the vehicle density in the study area is 0.005446 vehicle s/m² of the land in urban

non-built up areas, and 0.0313 vehicles/m² of the street in urban built up areas. The higher

vehicle density in streets is explained by the fact that most of the cars in these two towns

are parked in streets.

Table 3.1 Characteristics of the vehicles in the study area

Characteristic

Type of Vehicle i

Smaller cars

Seat Ibiza

Compact

Vehicles

Seat León

Small SUVs

Peugeot 2008

Medium-sized

SUVs and larger

vehicles

Volksw. Tiguan

Length (m) 3.68 4.18 4.16 4.43

Width (m) 1.61 1.74 1.74 1.81

Height (m) 1.42 1.44 1.56 1.67

Clear distance from

ground (m) 0.12 0.12 0.17 0.18

Density (kg/m³) 108.00 125.86 104.41 115.26

Proportion gi (%) 26 32 15 27

3.4.3 Vehicle stability thresholds

First, the vehicles’ stability thresholds of the four vehicle types representing the vehicle

fleet were determined. With the physical characteristics of these vehicles and by

employing Equations 3.1, 3.2 and 3.3, the velocity from which each vehicle would lose

its stability was calculated for each water depth. The obtained results are shown in Figure

3.6. The part of the graph over the threshold of each vehicle corresponds to the unstable

zone; that is, the area where vehicles would destabilize. The part of the graph below the

threshold corresponds to the stable zone; that is, the area where vehicles would remain

stable.

The analysis of this graph indicated that the thresholds of the bigger vehicles exceeded

those of the smaller vehicles; that is, for a given water depth, bigger-sized cars would


29

remain stable at faster velocities than at the velocities guaranteeing smaller cars’ stability.

As expected, this meant that larger vehicles would be more stable during flooding.

Moreover at fast flow velocities, the water depths at which vehicles would destabilize

displayed asymptotic behaviour and came close to the clear distance value between the

chassis and the ground. For slow velocities, the water depths that brought about vehicle

destabilization tended to move closer to the values at which the vehicle would float under

conditions when water was still.

Figure 3.6 Stability thresholds for each vehicle type

3.4.4 Vulnerability

As previously indicated, the two vulnerability components were represented by exposure

and susceptibility. Exposure was determined by the proportion of each vehicle type in

fleet gi (Table 3.1), and by vehicle density d, which took different values for urbanized

areas that had, and had not, been built-up (see Subsection 3.4.2). With these density

values, the total number of vehicles driving around and/or parked in the flooded areas for

the flood swell with a 500-year period equalled 18.205.

Susceptibility was established with the damage function, which was calculated using the

vehicle instability index Si values (see Subsection 3.3.2). For a better spatial

representation and to facilitate their interpretation, on the hazard maps obtained for each

studied vehicle type, these vehicle instability indices were divided into the following five

ranges according to stability: a) range 1: indices below zero, corresponding to the sectors

in which vehicles would lose stability due to floating; b) range 2: indices between 0.0 and

0.5, denoting that vehicles would probably remain stable; c) range 3: indices between 0.5

and < 1.0, meaning that vehicles would probably remain stable, but would be about to

Unstable Zone

Stable Zone

0,00

0,05

0,10

0,15

0,20

0,25

0,30

0,35

0,40

0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5 5,0

Dep

th (

m)

Velocity (m/s)

Utilitary Compact Small SUV Medium SUV

Stable Zone

Unstable Zone


30

destabilize owing to the sliding phenomenon; d) range 4: indices between 1.0 and 1.5,

corresponding to the sectors in which vehicles would destabilize owing to sliding

phenomenon; e) range 5: indices > 1.5, representing those sectors in which vehicles would

greatly destabilize owing to sliding phenomenon.

According to Equation 3.5, damage function D(Si) took a value of 1 when the hazard

indices had negative values (range 1), and equal to or greater than 1 (ranges 4 and 5). The

damage function value equalled 0 in all the other cases (ranges 2 and 3).

Finally, the vulnerability for vehicle type i at a point on the territory was calculated by

multiplying the proportion of a vehicle type in the fleet, gi, by vehicle density, d, by the

damage function value, D(Si), as set out in Equation 3.6.


The collected flood hazard data was provided by the Confederación Hidrográfica del

Júcar (Júcar Hydrographic Confederation; CHJ, 2011), which employed the model

Infoworks 2D to calculate the levels and velocities of flow in the flooded area. Flood

hazard maps corresponding to floods with return periods of 10, 25, 50, 100 and 500 years

were available. The floods with return periods of 10 and 25 years were found to not affect

the study area. This was why a Tmin value equalling 37.5 years was defined, which

corresponded to the average of both the last return period with data available indicating

that the study area had not been flooded (25 years) and the first return period with data

available reporting that the study area had been flooded (50 years).

Figure 3.7 presents the maximum water depth maps and their velocities corresponding to

the flooding with the 100-year return period. For some sectors of the study area, it shows

that the flow depths for this event exceeded 3.0 m (panel a in Figure 3.7) and velocities

went over 3.0 m/s (panel b in Figure 3.7).

Figure 3.7 Flood hazard: maximum water depths and their corresponding flow velocities

in the study area due to the Rambla del Poyo flooding with a 100-year return period

Source: Confederación Hidrográfica del Júcar (2011)

a. Depths b. Velocities


31

The vehicle instability hazard was calculated with the expression provided in Equation

3.3 and the procedure graphically represented in Figure 3.2. As the vehicles representing

the vehicles fleet presented different characteristics, a hazard map was calculated for each

vehicle type and every analysed flood. In order to determine vehicle instability index Si,

it was assumed that cars were completely water tight and lay perpendicularly to the flow,

which usually represents the most unfavourable condition because the cross-sectional

area exposed to the flow and, consequently, the hydrodynamic force applied to vehicles,

are maximized (Smith et. al, 2017).

By way of example, Figure 3.8 presents the hazard maps of vehicle instability obtained

for Seat Ibiza (represents smaller vehicles) by considering floods with return periods of

50 and 500 years. In most flooded areas, the vehicle instability index values were below

0.5 and negative values predominated. A similar behaviour was noted on the other

instability hazard maps created for the other vehicle types and return periods.

a. Tr = 50 year b. Tr = 500 years

Vehicle unstability index Si

Loss of floating stability Stable zones Loss of sliding stability

<0 0 – 0.5 0.5-1 1– 1.5 >1.5

Figure 3.8 Hazard maps of vehicle instability in the study area for floods with return

periods of 50 and 500 years for Seat Ibiza

The analysis performed with the results obtained for all the vehicles and return periods

indicated that the Rambla del Poyo floods with return periods exceeding 50 years posed

a major hazard for the vehicles being driven or parked in the built-up areas of Massanassa

and Alfafar because even bigger vehicles would lose their stability in most flooded areas

(Si < 0 or Si ≥ 1). With medium-sized SUVs and larger vehicles, represented by

Volkswagen Tiguan, both water depths and flow velocities would destabilize these

vehicle types in 66% of the flooded areas due to flooding with a 50-year return period.

This percentage would rise to 74% if the behaviour of smaller cars (represented by Seat

Ibiza) was evaluated during the same event. When a flood with a 500-year return period

was considered, the percentages of areas in which vehicles would destabilize would rise

to 76% for medium-sized SUVs, and up to 80% for smaller vehicles.


32

As a result of the high flow depth values shown in most of the flooded zones in the study

area, loss of stability of all the studied vehicle types would be mostly attributed to the

floating phenomenon (Si < 0), while the sliding phenomenon would have less impact (Si

≥ 1). For instance, with smaller vehicles: as the corresponding floods would present a

500-year return period (panel b in Figure 3.8), the floating phenomenon would cause

vehicle destabilization in 79% of flooded areas, whereas the sliding phenomenon would

do so in only 1% of these areas. Similar behaviours to this were observed for the

remaining return periods and other vehicle types.

Moreover it is worth pointing out that in percentage terms, the flooded areas that were

safe for vehicles lowered as flooding frequency reduced and flooding intensity rose. For

example, with smaller vehicles (Seat Ibiza), for flooding with a 50-year return period, 104

hectares (ha) would be flooded and cars would remain stable in 26% of them. However

for the flooding with the 100-return period, 174 ha would be flooded and vehicles would

remain stable in only 26% of them. For the flooding with a 500-year return period, 193

ha would be flooded and vehicle stability would remain in only 20%.

As expected, in accordance with Figure 3.6, and given their bigger size and the longer

free distance between their chassis and the ground, medium-sized SUVs (the biggest

vehicle type herein included) would be the safest because they would remain stable in

larger-sized flooded areas than the other vehicle types. The size of the flooded areas in

which vehicles would conserve their stability would progressively reduce with vehicle

size to its lowest for smaller vehicles.

3.4.6 Vehicle instability risk

The instability risk for each vehicle type was calculated using the expression in Equation

3.8 and the procedure depicted in Figure 3.4. The instability risk maps obtained for each

employed vehicle type are shown in Figure 3.9, without considering their proportion in

the vehicle fleet. The analysis of these maps indicated that as vehicle size increased, the

areas with a higher instability risk (streets) diminished and, consequently, the low-risk

areas increased. This result was expected because, as indicated in Section 3.4.5, the bigger

the car size, the greater its stability during floods.

Figure 3.10 shows the risk map of total instability, which was obtained by summing the

risk maps of each vehicle type, multiplied by their proportion in the vehicle fleet. It is

noteworthy that in streets, where vehicle density exceeded the density of all the other

urban areas by almost 6-fold, higher values were given for the instability risk (of the order

of 8.4 cars per ha per year). These values were much higher than those for the existing

risk in the other flooded areas. These relatively high-risk areas corresponded to about 8%

of the whole flooded area. In an area that roughly equalled 60% of the flooded area, the

risk for vehicles was relatively low with values below 1.4 cars per ha/year.

Table 3.2 shows the annual number of cars at risk of being dragged by the flood flow

according to two hypotheses: (i) the vehicle fleet was represented by a single vehicle type

(column 2); (ii) the vehicle fleet was represented by all four vehicle types indicated in

Subsection 3.4.2 (column 3). When the data in column 2 were analysed, once again it was

concluded that bigger vehicles (i.e. medium-sized SUVs) were the most stable vehicle


33

type during flooding as they posed fewer at-risk vehicles for instability. The smaller

vehicles (Seat Ibiza) were the least stable cars by presenting the most at-risk number of

vehicles.

a.- Smaller Vehicles b.- Compact Vehicles

c.- Small SUVs d.- Medium SUVs

Risk (Car/Hectare/year)

0.0 – 1.4 1.4 – 2.8 2.8 – 4.2 4.2 – 5.6 5.6 – 7.0 7.0 – 8.4

Figure 3.9 Risk map of instability for each vehicle type studied in the study area

without considering their proportion in the vehicle fleet

By analysing the data in column 3, it was concluded that compact vehicles (i.e. Seat León)

posed the highest risk, which correspond to roughly one third of all the at-risk vehicles.

This was because, despite not being the most unstable cars, they had the highest

proportion in the vehicle fleet. The smaller (least stable) vehicles presented a slightly

lower risk than compact vehicles as their proportion in the vehicle fleet was also lower.

The vehicles with the lowest instability risk in the study area corresponded to small SUVs

because they were one of the most stable vehicle types with the lowest proportion in the

vehicle fleet compared to the other studied vehicle types. For this reason, this vehicle type

only represented about 15% of all the at-risk vehicles.


34

Figure 3.10 Map of the instability risk for vehicles in the study area

Table 3.2 Mean annual number of at-risk vehicles for instability in the whole

study area in line with the two fleet hypotheses: only one type and with the

present proportion

Vehicle type

Mean annual number of at-risk vehicles

Representation of the fleet

A single vehicle type The four vehicle types

and their proportions

Smaller vehicles 276.5 71.9

Compact vehicles 269.7 86.3

Small SUVs 252.7 37.9

Medium-sized SUVs and

larger vehicles 244.1 65.9

Total - 262.0

3.4.7 Sensitivity analysis to Tmin

Bearing in mind the high uncertainty for the return period value from which the study

area started being flooded (known in this methodology as Tmin), the sensitivity of vehicle

instability risk to the values of this parameter in the study area was determined. Given

that, according to available flood maps, the 25-year return period flood envelope does not

reach the study area, unlike the 50-year return period flood which does, the Tmin values

adopted 30, 35, 40 and 45 years, and 37.5 years was the value employed to implement the

methodology.

Risk (Car/Hectare/year)

0.0 – 1.4

1.4 – 2.8

2.8 – 4.2

4.2 – 5.6

5.6 – 7.0

7.0 – 8.4


35

Figure 3.11 offers the obtained results. The conclusion drawn from studying this graph

was that a linear relation appeared between the exceedance probability of the event

corresponding to Tmin and the number of at-risk vehicles; the more the probability of the

event considered to be Tmin occurring, the more the at-risk vehicles. Furthermore, Tmin

significantly influenced vehicles’ instability risk values. In relation to the value taken for

the methodology implementation, the number of at-risk vehicles dropped by

approximately 12% when taking a 45-year Tmin value, and rose by about 17% when taking

a 30-year Tmin value.

Figure 3.11 Number of cars at risk of instability in the study area when considering

different Tmin values

3.4.8 Final Remarks

Applying the methodology to the selected case study allowed us to observe that the

vehicle instability risk due to flood events in the towns of Massanassa and Alfafar is

relatively high in streets given the values of about 8.4 cars per ha/year in them. Larger

vehicles (e.g. medium-sized SUVs) would be the most stable vehicle type, while smallest

vehicles, represented by smaller vehicles type, would be the least stable. Nonetheless,

given the employed fleet proportions, the vehicle type at highest risk is compact cars,

whereas the vehicle type at the lowest risk is small SUVs.

The Rambla del Poyo floods with return periods of 50 years or longer are a major hazard

for the vehicles located in the study area because they would destabilize in most of the

flooded area. The most damaging effect would result from the vehicle floating

phenomenon owing to the vertical ascending pushing caused by flows from overflowing

rivers, which would present relatively high water depth values. Loss of vehicle stability

owing to the sliding phenomenon would occur in relatively small areas.

200

220

240

260

280

300

320

0,02 0,0225 0,025 0,0275 0,03 0,0325 0,035

Ris

k (

Car/

year)

Exceedance probability (1/Tmin)

1/45 1/40 1/37.5 1/35 1/30

Linear relation


36

The developed methodology provides a detailed vision of the vehicle instability risk due

to flooding in a given area. The results of the described methodology allow to precisely

locate not only the areas posing a higher risk for vehicles (for both vehicle type and the

for entire existing vehicle fleet), but also safe zones. Consequently, the implementation

of this methodology could be very useful for the entities in charge of planning the territory

in order to design measures that contribute to reducing the adverse effects of floods.

Chapter 4, Determining the vehicle instability risk in stream crossings

37

4. DETERMINING THE VEHICLE INSTABILITY RISK IN STREAM

CROSSINGS

4.1 Introduction

Despite the fact that floods negatively affect vehicles, there are few studies available that

attempt to determine the risk to which cars are subjected during river floods. The Word

Bank Group (Rogelis Prada, 2015) presented a simple equation to calculate risks on road

networks owing to floods. In this equation, risk is expressed as either number of deaths

per year or economic cost per year, which is obtained with the summation of the product

of the following factors: (i) hazardousness, understood as the probability of a threatening

event happening; (ii) exposure, understood as the probability of vehicles being affected

by the threatening event; (iii) vulnerability, which ranges between 0 and 1, and indicates

the severity of the expected damage; (iv) total potential loss, which is expressed as the

number of people who died or economic costs.

Of the few studies that have centred on studying risk components specifically in stream

crossings, we find that presented by Michielsen et al. (2016). By analysing physical basin

characteristics by implementing statistical methods, these authors developed a

methodology that could predict if stream crossings in a given area were flood-prone.

Another similar study was conducted by Kalantari et al. (2019) which, based on

multivariate statistical modelling, proposed a methodology to determine the probability

of floods occurring in stream crossings. This methodology was also based on physical

basin characteristics.

A methodology was herein developed that allows the vehicle instability risk to be

estimated. This risk is posed by the growing river levels for vehicles when they cross

stream crossings, which may correspond to fords, vented fords and bridges. We stress that

this methodology can be used on bridges whose decks might be flooded, and whose

structures would not hypothetically fail structurally during flooding.

This chapter article firstly presents a brief description of the mechanisms that lead to loss

of vehicle stability. Then it describes the methodology developed to obtain the instability

risk posed for those vehicles driving through a stream crossing. This risk is calculated by

the discrete solution of the statistical integral of the product of hazard by vulnerability,

which is a more elaborate calculation that those presented in former studies. Finally, it

implements this methodology in the Godelleta municipality (Spain), where 32 stream

crossings are identified.

4.2 Methodology

The vehicle instability risk due to floods in stream crossings (R) corresponds to the annual

mean number of vehicles whose stability would be lost when crossing these places

According to Equation 3.4 the risk is determined by the statistical integral of the

instability hazard and vehicles’ vulnerability. The procedure that must be followed to

calculate the hazard, vulnerability and, finally, the instability risk of vehicles in stream

crossings, is presented below.


38


The flood hazard for vehicle i in a stream crossing is obtained by combining the

probability of a flooding event taking place with the values that the vehicle instability

index, Si, would take, as shown in Figure 3.3, panel C. The details to obtain the hazard

are found in the chapter 3, section 3.3.1, for a flooding zone where there are flooding

maps for different return periods. With stream crossings, it is sufficient to employ the

maximum annual flow quantiles for a set of return periods and to convert this discharge

into water depths and velocities by a 1D hydraulic stationary model with an adequate flow

hypothesis (critical flow, uniform flow, etc.).

4.2.2 Vulnerability

As already noted, vulnerability depends on the degree of the elements that can be affected

by flooding from being exposed, and by their susceptibility. The following subsections

indicate how susceptibility and exposure should be calculated.

4.2.2.1 Susceptibility

Susceptibility indicates the degree of damage that elements exposed to flooding can suffer

and is normally expressed by damage or loss functions. In this methodology,

susceptibility was established through the damage function described in Section 3.3.2. A

graphical representation of the way this function is defined and found in Figure 3.4, panel

B.

4.2.2.2 Exposure

In the problem being solved, exposure was the number of each vehicle type i that could

cross the stream crossing while water levels rose. Since the duration of the flood increases

as its return period T increases, the number of potentially affected vehicles type i. Ni will

depend on the return period and can be denoted as Ni(T).

If the vehicle traffic distribution was the Poisson type, which has been applied to low and

medium vehicle flows (Cal y Mayor and Cardenas, 2007), it is possible to demonstrate

that the number of vehicles, Ni(T), corresponds to the following expression:

𝑁𝑖(𝑇) = 𝑞 𝑔𝑖 ∆𝑡𝑖(𝑇) [4.1]

where q corresponds to the vehicle type i traffic in the stream crossing during a flood. If

no further information is available, Average Daily Traffic (ADT) can be used; gi is the

proportion of vehicles type i in the fleet; ∆ti(T) corresponds to the time interval during

which flows can affect the stability of vehicles type i during the flood with return period

T.

Time interval ∆ti(T) depended on the vehicle type because hazard was defined for the Si

of the flood peak and instability could take place for smaller flows. In the case study, one

calculation method will be shown in more detail.


39

The relation between Ni(T) and return period T corresponded to exposure. The graphical

representation of this exposure is found in Figure 4.1, panel B.

In fact the time interval ∆ti(T) during which the flood could affect exposed vehicles’

stability was in accordance with drivers’ behaviour. The present methodology

contemplated two different drivers’ behaviours: (i) drivers did not decide to stop before

crossing during floods; (ii) for safety reasons, drivers decided to stop driving through the

flooded area when the water depth exceeded a given value, which was called a limit water

depth, and would not cross the stream crossing during the rest of the flood (the resulting

value was lower than the previous one and in accordance with this limit water depth).

To calculate risk, it is necessary to express vulnerability according to hazard. So an

instrumental function is required, which is called the exposure function of vehicles type

i, Ni(si), and was obtained by combining hazard and exposure, as depicted in Figure 4.1.

This figure shows that, as previously indicated, a vehicle instability index Si corresponded

to each event with a given probability (Hazard, panel A) and a number of vehicles Ni

driving through the stream crossing (Exposure, panel B). In this way, it was possible to

relate the vehicle instability index Si to the corresponding numbers of vehicles Ni, which

gave a similar graph to that found in panel C with the vehicles’ exposure function.

Figure 4.1 Outline of the process to follow to determine the exposure function of

vehicles type i

Num

ber

of

vehic

les t

ype i (

Ni)

Number of vehicles type i (Ni)

1

0

Vehic

le insta

bili

ty in

dex (

Si)

A. Hazard Si (T) C. Exposure function Ni (si)

B. Exposition Ni (T)



Instability

0

Vehic

le insta

bili

ty in

dex (

Si)

1

Stability


40

Finally, the vulnerability for vehicles type i, Vi, was obtained by combining the Di(si)

damage and exposure Ni(si) functions, as shown in Figure 4.2. This figure once again

shows that to each vehicle instability index Si corresponds to a value of the damage

function Di(si) (panel A) and a value of the exposure function Ni(si) (panel B). When

graphing the vehicle instability index against the product of its corresponding values of

Damage Di(si) and Exposure Ni(si) function, a similar graph to that presented in panel C

was obtained, which represents the vulnerability of the vehicles. This vulnerability was

expressed as a function of the vehicle instability index Si, which is why it was denoted as

Vi(si) and was measured in number of destabilised vehicles.

Figure 4.2 Outline of the procedure to follow to obtain vulnerability of vehicles type i

in the event of floods


The instability risk was calculated by replacing the expressions obtained for both the

hazard and vulnerability of the vehicles driving through a stream crossing in Equation

3.4. Figure 4.3 outlines the procedure that must be set up to calculate the instability risk

for flooding of vehicles type i in stream crossings. Panel A corresponds to the instability

hazard, which was obtained following the procedure described in Section 4.2.1. Panel B

corresponds to vulnerability, which was obtained as set out in Section 4.2.2. When hazard

was combined with vulnerability, for each flooding event with a given probability of

occurring, a corresponding number of vehicles Ni would lose their stability in stream

crossings. When creating a graph to depict the probability of each event occurring with

the respective number of vehicles that would lose their stability, a similar graph was

obtained to that shown in panel C. The instability risk corresponded to the area under the

curve, which was formed when joining the values of those vehicles that would lose their

stability during each flood event.

A. Damage function Di (si) B. Exposure function Ni (si) C. Vulnerability Vi (si)

Number of vehicles type i (Ni)

0

1

Damage (Di) 1 0



Vul

Vehic

le insta

bili

ty in

dex (

Si)

Vehic

le insta

bili

ty in

dex (

Si)

Vehic

le insta

bili

ty in

dex (

Si)


41

Figure 4.3 Outline of the process that must be set up to calculate the instability risk for

flooding vehicles type i in a stream crossing

As Equation 3.4 contemplates a vehicle type i, the total risk was obtained when using the

summation of the partial risk obtained for each vehicle K type with which the fleet was

represented. So the total risk would be:

[4.2]

In practice it is not possible to calculate and obtain the integral of Equation 4.2 as we did

not work with analytical functions and had a limited M number of flood maps. A discrete

approach could be as follows:

[4.3]

where j corresponds to the number of the order of flood maps, which varied from 0 to Tmin

up to M for Tmax, with Tmin being the lowest return period from which vehicles would start

being affected; Tmax is the longest return period with an available flood hazard map; Vi(Si,j)

corresponds to the vulnerability of vehicle type i for a vehicle instability index Si during

the flood with return period Tj.

Vehic

le insta

bili

ty in

dex (

Si)

Ri

A. Hazard fsi (si) B. Vulnerability Vi (si)

C. Vulnerability Vi (T)


1

0

Num

ber

of

desta

bili

zed

vehic

les t

ype i

(Vi)



Vehic

le insta

bili

ty in

dex (

Si)



𝑅 = ∑ 𝑅𝑖

𝐾

𝑖=1

= ∑ ∫ 𝑉𝑖(𝑠)𝑓𝑆𝑖(𝑠)𝑑𝑠

∞

0

𝐾

𝑖=1

𝑅 = ∑ {[ ∑𝑉𝑖(𝑠𝑖,𝑗) + 𝑉𝑖(𝑠𝑖,𝑗+1)

2(

1

𝑇𝑗−

1

𝑇𝑗+1)

𝑀−1

𝑗=0

] + 𝑉𝑖 (𝑠𝑖,𝑀) (1

𝑇𝑀)}

𝐾

𝑖=1


42

The last term in Equation 4.3 corresponds to the residual risk for longer return period

events than Tmax, for which the same vulnerability as Tmax was assumed.

4.3 Application to a case study

The developed methodology was employed to determine the vehicle instability risk for

flooding in the stream crossings found in the Godelleta municipality, which lies very close

to the Spanish Mediterranean coastline (Figure 4.4). This allowed the applicability of the

methodology to be determined. For the case study, it permitted the influence of both

drivers’ behaviour and the degree of obstruction of vented fords on the results to be

analysed.

Figure 4.4 Location of the Godelleta municipality, ravines, main roads

and its built-up area

4.3.1 Characterisation of the study area

The Godelleta municipality covers 37.5 km², has a population of 3,441 inhabitants, is

relatively flat with gentle slopes, and a mean height of 266 masl. Its climate is semiarid

Mediterranean with very variable mean precipitation figures around 450 mm, and rainfall

concentrates in spring and autumn months.

The Godelleta municipality lies in the middle of the Rambla del Poyo Basin, which is an

intermittent 43.5 kilometre-long current that begins to flow at a height of 1,023 masl and

flows into the Albufera lagoon. The basin covers 430 km². Its slope varies between 16%

at the highest point and 2% in the lowest part, where flash flooding occasionally occurs

in autumn months (Salazar, 2013). This municipality has a drainage network made up of

several intermittent water currents that flow westerly-easterly of a torrential nature, with

maximum flows in spring and autumn (Terrasa et al., 2018).


43

This municipality’s road network is relatively dense and formed by regional and local

roads in good condition. Regional roads include roads CV-50, CV-416, CV-417 and CV-

424 (Fig. 4.4). The last three roads are B-roads (single lane for each direction) that are

relatively narrow with no verges. Road CV-50 is also a B-road, but has ample verges on

both sides.

The intersection between the drainage network and the road network involves 32 stream

crossings. The vehicles driving through these crossings via these roads would be at risk

for instability due to floods that could occur in ravines. Of these 32 stream crossings,

eight correspond to fords, 18 to vented fords and six to bridges. In this paper, the risk in

the stream crossings corresponding to fords and vented fords was calculated because the

drainage capacity of these bridges corresponds to very little exceedance probabilities and,

therefore, the risk of vehicles being dragged away is negligible. Figure 4.5 presents the

location of the analysed fords and vented fords.

4.3.2 Characterisation and exposure of the vehicles driving through the study area

The characterisation of the vehicles found in the study area was done using the

information presented in the Section 3.4.2. The vehicles selected to represent the fleet of

cars circulating in the municipality of Godelleta and their characteristics are presented in

Table 3.1.

The traffic data for roads CV-416, CV-417 and CV-424 were taken from the official

traffic levels of the Valencian Council Offices (2018). The road traffic data for road CV-

50 was acquired from the information reported by the Generalitat Valenciana (2019). The

ADT (number of vehicles/day), reported by these institutions for the sites of interest for

this study, were as follows: (i) CV-50: 5141; (ii) CV-416: 380; (iii) CV-417: 484; (iv)

CV-424: 7369. No official traffic levels data were available for local roads.


The flows corresponding to the floods in the ravines found in the study area were

determined by interpolation techniques using existing flow data about Rambla del Poyo

at several basin points for return periods of 1, 2, 5, 10, 25, 50, 100 and 500 years. The

flows of all the stream crossings were interpolated using the expression proposed by

Leopold et al. (1964), which allows floods with drainage areas and their corresponding

return periods to be related:

𝑄𝑇 ∝ 𝐴𝑑𝑏 𝑇 [4.4]

where QT is the peakflow quantile, Ad is the drainage area in each stream crossing, b is an

exponent which, according to Leopold et al. (1964), varies between 0.65 and 0.80, and T

is the return period. With the Rambla del Poyo fit, the determination coefficient

significantly increased if an exponent was included in the return period. The final

outcome used to estimate the flow quantiles at any point of Rambla del Poyo (including

the ravines in the Godelleta municipality) was this expression:


44

𝑄𝑇 = 0.4929 𝐴𝑑0.75 𝑇0.6512 [4.5]

where QT is given in m³/s, Ad in km² and T in years.

The water levels and velocities corresponding to each analysed flow at the sites of interest

were calculated using the hydrodynamic modelling of the floods that flowed through

ravines by taking a unidimensional stationary flow hypothesis in a river section that

included the stream crossing. These modellings were done with the HEC - RAS model, a

widely used software in hydraulic engineering. In these modellings, the geometric

representation of the riverbed was performed with the cross-sections obtained from the

digital elevations model of the Spanish National Centre of Geographic Information of

Spain for all Spanish territory (http://centrodedescargas.cnig.es/CentroDescargas/

index.jsp#, last consulted in September 2019) and based on the field trips of August 2019.

The geometry of the fords and vented fords was obtained during field trips.

With the results obtained with the performed modelling, and having implemented the

procedure described in Section 3.3.1, instability indices Si were calculated for each

analysed vehicle type for the different defined return periods. These indices were

calculated by assuming that vehicles were completely watertight and lay perpendicularly

to the flow. Table 4.1 presents the instability indices Si obtained for the different vehicle

types in all the stream crossings, but only for the flow with the 50-year return period.

The obtained vehicle instability indices Si indicated that the flows with return periods that

equalled or exceeded 50 years posed a high risk for the vehicles driving through stream

crossings because, for a flood with a 50-year return period, the vehicle stability of roughly

55% of the vehicles would be lost. This percentage also had a significant value for the

flood with a 25-year return period because it came close to 45%, and it almost reached

90% for a 500-year return period.

4.3.4 Vulnerability

Vulnerability was calculated by combining susceptibility and vehicles’ exposure to

floods. Susceptibility was established through the damage function defined in Section

4.2.2.1. The damage function values either equalled 1 for flooding events in which vehicle

instability index Si had negative values (destabilisation due to floating) or exceeded or

equalled 1 (destabilisation due to dragging). When vehicle instability index Si had positive

values below 1, the damage function equalled 0.

The exposure function was determined by bearing in mind that, according to that

established in Section 4.2.2.2, for a given flooding event, the number of vehicles type i

exposed to floods, Ni would correspond to the mean number of cars i that would drive

through the flooded site during time interval ∆ti when the conditions leading to vehicle

instability would take place. To know the duration of this time interval, we calculated the

flood duration and times when the flow hydrodynamic conditions that would cause loss

of vehicle stability would start and stop.

The flood duration time in the studied ravines was calculated by summing the duration

time of rainfall events and the concentration time in each basin. The rainfall duration time

was obtained from subtracting the concentration time for Rambla del Poyo from its mean

http://centrodedescargas.cnig.es/CentroDescargas/%20index.jsp

http://centrodedescargas.cnig.es/CentroDescargas/%20index.jsp


45

flood duration time. According to Salazar (2013), the mean flood duration of Rambla del

Poyo approximately equalled 12 hours in the hydrometric station called Rambla del Poyo,

where the drainage area equalled 184 km².

The concentration time, tc, of both the Rambla del Poyo Basin and ravines was calculated

by the following expression proposed by the Generalitat Valenciana (2018):

𝑡𝑐 = 0.7073 𝐴𝑑0.4963

[4.6]

Table 4.1 presents the flood duration times of the ravines found in the study area, which

were obtained by summing the rainfall duration time and the concentration time up to

each stream crossing.

The water levels and flow velocities at which the analysed vehicle types would

destabilise, and the time interval ∆ti during which stability would be lost in each flooding

event, were determined by the results obtained with the hydrodynamic models developed

for the stream crossings and the calculated vehicle instability indices Si. Time interval ∆ti

was calculated by contemplating the two possible drivers’ behaviours set out in Section

4.2.2.2. For calculating under the condition for which it was assumed that drivers would

decide to stop at a given time during the flood, a limit water depth equal to 0.3 m was

adopted to interrupt the vehicle traffic.

The number of vehicles type i exposed to floods, Ni, was calculated by multiplying the

vehicle traffic flow, q, by the proportion, gi, of vehicles type i in the fleet, by the time

interval, ∆ti, during which the conditions that would result in vehicle instability taking

place. If official traffic levels data were available for roads, these data were used.

However, if they were not available for some roads, then the vehicle levels recorded

during field trips were employed. Table 4.1 shows the hourly flow of the vehicles in all

the stream crossings.

The exposure function was obtained by relating the vehicle instability index Si calculated

for each flooding event to the corresponding number of exposed vehicles Ni.

Finally, vulnerability was calculated by multiplying the results obtained by the damage

and exposure functions for each flooding event.


The vehicle instability risk was calculated by implementing the procedure described in

Section 4.2.3. The risk obtained by considering that drivers would stop when flow depth

reached the limit water depth was called actual risk, while that obtained by contemplating

that drivers would not stop at any time was called estimated potential risk. Table 4.1 offers

the values obtained for the estimated actual/potential risks. Figure 4.5 graphically

represents the estimated actual risk; with the sole objective of making this representation,

this risk was subjectively classified as high for the values that equalled or exceeded 0.2

vehicles/year, medium when ranging between 0.1 and below 0.2 vehicles/year, and low

if below 0.1 vehicles/year.


46

Table 4.1 Vehicle instability risk due to floods in the stream crossings of the

Godelleta municipality

Stream

crossings Stream

Stream

crossings

with culvert

Traffic

flow q

(cars/

hour)

Flood

duration

(hours)

Flood Tr 50 años

Instability

risk (cars/year)

Dis-

charge

(m³/s)

Hazard index Si

Actual Poten-

tial

Vehicle type

Small

cars

Com-

pacts

SUVs

small

SUVs

med.

1

Del

Murtal

Yes 45.32 6.2 73.71 -0.42 -0.43 -0.45 -0.52 0.35 4.67

2 Yes 0.50 6.1 70.80 -0.14 -0.14 -0.14 -0.15 0.21 1.85

3 Yes 1.51 6.0 67.68 -0.26 -0.25 -0.26 -0.28 0.22 3.80

4 No 1.01 5.5 53.55 -0.86 -0.82 -0.86 -0.90 1.12 2.37

5 Yes 1.51 5.3 47.71 -0.22 -0.21 -0.22 -0.23 0.11 2.99

6 No 0.21 4.7 33.13 -0.13 -0.12 -0.13 -0.13 0.11 0.46

7 Yes 214.21 4.7 32.96 0.00 0.00 0.00 0.00 0.16 2.21

8 Yes 4.03 4.4 25.72 -0.21 -0.20 -0.21 -0.23 0.65 2.13

9 Yes 6.04 3.8 13.41 -0.22 -0.21 -0.22 -0.24 0.08 1.56

10 No 3.02 3.5 8.58 -74.99 26.73 7.79 3.80 0.39 0.48

11 No 0.33 3.0 2.87 -0.72 -0.89 -1.14 -4.20 0.01 0.02

12 Del Bo-

rreguero Yes

0.33 3.0 3.02 0.00 0.00 0.00 0.00 <10-4 <10-4

13 Del

Gitano

Yes 6.04 3.6 11.33 -0.56 -0.69 -0.88 -3.23 0.02 0.29

14 No 0.32 3.1 3.84 10.13 1.58 0.58 0.31 1*10-3 0.01

15 Del Moro Yes 214.21 4.2 21.73 0.00 0.00 0.00 0.00 0.20 1.15

16 Barran-

quet

Yes 0.28 3.6 10.36 0.11 0.09 0.01 0.00 2*10-4 0.004

17 Yes 96.42 3.4 7.84 0.00 0.00 0.00 0.00 5*10-4 0.001

18

Del

Juncar

Yes 307.04 3.8 14.08 0.03 0.03 0.00 0.00 0.18 3.71

19 Yes 12.08 3.8 13.68 0.50 0.33 0.14 0.08 0.04 0.25

20 No 0.53 3.8 13.52 -0.36 -0.36 -0.37 -0.40 0.18 0.52

21 No 0.27 3.7 12.84 -0.02 -0.02 -0.02 -0.02 0.12 0.42

22 Yes 20.17 3.6 10.58 0.05 0.05 0.00 0.00 0.02 0.20

23 Yes 15.83 3.1 4.16 0.00 0.00 0.00 0.00 3*10-4 3*10-4

24 De

Pelos

Yes 15.83 3.7 13.15 0.51 0.33 0.14 0.09 0.04 0.33

25 No 0.28 3.5 9.86 -0.55 -0.60 -0.65 -0.93 0.003 0.04

26 Yes 271.75 3.2 5.86 0.00 0.00 0.00 0.00 <10-4 <10-4

NB: the locations of the intersection points are found in the Figure 4.5

The analysis of the results concluded that the actual vehicle instability risk in the stream

crossings in the Godelleta municipality was high for 27% of the existing intersections,

medium for 23% of these stream crossings and low for the remaining 50%.

When analysing the results obtained by considering that vehicle traffic would continue

moving throughout flood duration (potential risk), we observed that the values would be

2-fold higher than those obtained after considering that vehicle traffic would cease at a

given time. Accordingly, 69.2% of the stream crossings would obtain values above 0.2

vehicles/year and only 26.9% of the stream crossings would have values below 0.1

vehicles/year.


47

It is highlighted that most of the El Murtal Ravine stream crossings were at risk for vehicle

instability. This risk can be considered medium or high, explained by this ravine having

the biggest drainage area and greater flows inland of the Godelleta municipality. This

condition coincides with the conclusion drawn by Versini et al. (2010), who evaluated

the susceptibility of roads to flash floods in a sector of France. These authors found that

the basin’s area size upstream of the stream crossing was a very important factor for

predicting floods in this sector.

NB: Risk values are found in Table 1

Figure 4.5 Vehicle instability risk due to floods in the stream crossings in the Godelleta

municipality

It is noteworthy that the instability risk for the vehicles on roads with low traffic levels

could be the same instability risk as those vehicles on roads with heavy traffic levels, as

in points 6 and 7, which corresponded to the intersections of the El Murtal Ravine with

the local road and road CV-50 with heavy traffic. These two stream crossings are

separated from one another by approximately 600 m, with risk values equalling 0.11 and

0.16 vehicles/year, respectively. This was because, despite road CV-50 presenting very

heavy traffic, vehicles would only be affected by floods with a 500-year return period.

Although the traffic levels on the local road are much lower, vehicles would be affected

by the floods corresponding to a 2-year return period.

According to the Generalitat Valenciana (2018), the diameter of the vented fords with

circular culverts must be no less than 1.0 m to avoid obstructions caused by materials

being dragged by flows. For the purpose of analysing the most unfavourable scenario

possible, this analysis determined the vehicle instability risk by assuming a 0.3 m limit

water depth and considering that the 10 vented fords with circular culverts whose

diameters were less than 1.0 m, or presented equivalent geometries, were completely

obstructed when flooding took place. Table 4.2 offers the results of this analysis. One

conclusion was made according to this information: in all cases, the instability risk

increased when culverts were obstructed or, in some cases, this increment could even


48

surpass 100%. This shows the importance of employing vented fords of suitable

dimensions and adequate maintenance to minimise the possibility of the vehicle

instability risk increasing.

Table 4.2 Vehicle instability risk by taking a limit water depth of 0.3 m and vented

fords with circular vents and a diameter less than 1.0 m, or equivalent geometries,

being unblocked or completely obstructed

Degree of

vented ford

obstruction

Vehicle instability risk (vehicles/year)

Vented Ford

2 3 5 8 9 12 13 19 22 23

Unblocked 0.21 0.22 0.11 0.65 0.08 2*10-6 0.02 0.035 0.017 0.0003

Completely

obstructed 0.39 0.47 0.13 0.87 0.26 3*10-6 0.07 0.042 0.018 0.0004

4.3.6 Influence of the limit water depth

The number of vehicles at risk for instability due to floods is directly related to the limit

water depth, and the risk becomes higher when drivers take poorly conservative attitudes.

Nonetheless, determining this water depth is clearly associated with uncertainty because

a large number of parameters influence decision making. For this reason, the effect of

variation in this water depth was studied on the values of the at-risk vehicles, for which

risk was determined by assuming water depths of 0.2 m, 0.4 m and 0.5 m, where 0.3 m

was the value taken while following the methodology. Figure 4.6 offers the obtained

results.

Figure 4.6 Number of vehicles at instability risk in the Godelleta municipality by

considering different water depth values from which vehicle traffic could cease

0.2 m 0.3m 0.4 m 0.5 m

0.3m


49

Our results indicated that the instability risk was extremely sensitive to the water depth

from which vehicle traffic stopped. When vehicle traffic was interrupted by a 0.2 m water

depth, the risk equalled zero for almost all the stream crossings. This behaviour did not

include the fords corresponding to points 6 and 10, where the risk values were 0.01 and

0.06 vehicles/year, respectively. When taking limit water depth values of 0.4 m and 0.5

m, we found that, in relation to the values obtained when following the methodology, the

mean risk value increased by almost 250% and 400%, while the maximum values rose by

almost 50% and 100%, respectively. As the minimum risk value did not undergo any

major modifications when the limit water depth varied by between 0.2 m and 0.5 m, as in

point 12 where vehicles would only be affected by flows with return periods exceeding

500 years.

The range of variation of the instability risk values for the different stream crossings

widened as the limit water depth value increased. The interquartile range equalled 0 m

when considering a limit water depth of 0.20 m. The interquartile range value was 0.20

m for a limit water depth of 0.3 m. It increased to 0.63 m with a 0.40 m limit water depth

and to 1.18 m with one of 0.50 m.

4.3.7 Final Remarks

The developed methodology was applied to the Godelleta municipality, and found that

roughly one quarter of the stream crossings in this study area presented a relatively high

vehicle instability risk due to floods because it exceeded 0.2 vehicles/year. Conversely,

the risk of approximately half these stream crossings could be considered relatively low

because it did not exceed 0.1 vehicles/year.

It was noteworthy that for road CV–50, where traffic levels are higher in the Godelleta

municipality, the instability risk values were lower than or equalled 0.2 vehicles/year,

which are low and medium values. This was because, as a result of the characteristics of

stream crossings, only the floods corresponding to long return periods would affect the

vehicles driving through flooded zones.

The methodology developed in the present study can be implemented by the organisations

responsible for town planning and road traffic to identify critical stream crossings in order

to contribute to vehicle stability and to take measures that allow the potential negative

impact of floods to lower.

Some of the measures that can be taken, and would contribute to cushion the impact of

floods, would be to, for instance, suitably maintain fords and vented fords, fit new culverts

or increase the size of existing ones. This would allow the lowest return period value from

which vehicles would be affected to increase, namely Tmin. Drivers’ good behaviour can

be encouraged by informing that they must stop when the flow depth in the stream

crossing reaches a certain limit water depth, which might allow the value of the time

interval during which flow could affect vehicle stability, namely ∆ti(T), to lower.

50

Chapter 5, Risk assessment of bridge failure due to river floods

51

5 RISK ASSESSMENT OF BRIDGE FAILURE DUE TO RIVER FLOODS

5.1 Introduction

Bridges are very important infrastructure works that are exposed to various natural

hazards, such as river floods, which can cause them to fail. The main causes of bridge

failures due to hydraulic actions include scour, structural deterioration, debris

accumulation, increased hydraulic loads and underpressure under the deck. Bridge failure

can be caused by damage to one or more parts of the substructure (foundation, piles and

abutments) or the superstructure (deck, supporting structure and accessories).

Owing to the disastrous consequences of bridge failures, determining the risk of these

structures due to flooding is critical for design purposes and the scheduling of

maintenance work. However, there have been very few studies on this topic to date. Most

of the studies available focus on determining the vulnerability of structures, but do not

assess the hazard or risk of bridges in the event of a flood.

These studies include the method proposed by Federico et al. (2003) to assess the

vulnerability of bridges to scour by considering the fluvial phenomena that govern the

fluvial dynamics of river floods. This method is based on the estimation of the maximum

scour depth in piles and foundations and on the analysis of the bearing capacity of the

pile-foundation-soil system. Vallés et al. (2011) proposed a methodology for assessing

the vulnerability of bridges over water currents to river floods, based on the analysis of

geomorphological, hydraulic-sedimentological and structural aspects. Hung and Yau

(2017) developed a method of rational vulnerability assessment of pile-supported eroded

bridges using a non-linear three-dimensional model that takes into account interactions

between bridge structures, water flow, soil and pile foundations

The works that seek to evaluate the risk of bridges due to floods include the methodology

presented by FHWA in 2002, which is actually an improvement of a methodology

presented by the same agency in 1994. In this method the relative annual risk of failure

due to erosion of a bridge is calculated as the product of the probability of failure by cost

associated with such event. Mondoro and Frangopol (2017) presented a methodology that

performs a benefit-cost analysis based on the risk of failure of bridges exposed to extreme

hydrological events; in this study the total risk is calculated as the sum of anticipated risks

according to the various potential failure modes of the structure.

This chapter developed a new methodology to determine the risk of bridge failure due to

flooding by analysing the integrity of the structure and the hydrological, hydraulic and

morphological characteristics of the water current and watershed. The main objective of

this methodology is to provide the necessary elements of judgement to order bridges

according to their level of risk and, therefore, the promptness with which the restoration

and/or maintenance work must be undertaken.

For this purpose, initially the types of failure that can occur on a bridge and their causes

are described. The developed methodology is then presented, indicating the procedure to

be followed to obtain the hazard, vulnerability and risk levels. Finally, the implementation

of this methodology in a set of bridges located on Spanish roads is presented and this case


52

study is used for a sensitivity analysis of the proposed values for vulnerability and the

return period from which the structure begins to be affected.

5.2 Failure of bridges over water currents

5.2.1 Typology of fails

The failure of a bridge is defined as the inability of the bridge to work according to the

parameters established during its design and construction in such a way that it cannot be

crossed or cannot be crossed safely. According to Wardhana and Hadipriono (2003), this

failure can correspond to: (i) a collapse when all or part of the structure falls down; (ii) a

deterioration when the structure or some of its components undergo wear that could or

could not lead to collapse.

The flow of a water current performs several hydrodynamic actions on a bridge and this

can generate different failure mechanisms that interact with each other (Mondoro and

Frangopol, 2017). These actions include underpressure and hydrodynamic pressure on

the deck, which could cause it to detach from the piles. This detachment can occur

vertically when the underpressure exceeds the capacity of the bridge in this direction or

in a transverse direction when the hydrodynamic pressures exceed the lateral resistance

of the deck-piles assembly.

Another failure mechanism occurs as a result of the overload imposed on the substructure

by the hydrodynamic pressures generated by the flow, which can lead to the piles failing.

In the same way, undermining near the bridge can cause structure failure due to

foundation failure or instability generated in the piles or abutment-foundation system

(Liang and Lee 2013).

According to Mondoro and Frangopol (2017), the interaction of these failure mechanisms

occurs, for example, when the action of the flow on the deck has not caused its failure but

generates an increase in the hydraulic loads on the piles and the foundation, increasing

the probabilities of failure of the latter; additionally, the contraction of the flow passing

under the deck can increase scour on the foundation of the structure.

Because the independent or combined failure of the deck, piles or foundation makes the

bridge unusable, the bridge is considered to have failed when any of these three parts have

failed.

5.2.2 Causes of failures

The failure of a bridge due to the action of a water current can be the result of multiple

causes, including scour, deterioration of materials, accumulation of debris and instability

of the stream. Scour is the most common cause of bridge failure during flooding as the

removal of material from the supporting soil reduces the bearing capacity of the

foundation and increases the load on the piles and abutments. (Yanmaz and Apaydin,

2012; Hung and Yau, 2017; Kim et al., 2017). Total scour is equal to the sum of general

scour, localized scour and local scour (Barbetta et al., 2017). General scour corresponds

to a decrease of the bed level in long sections of the watercourse due to the transport of


53

sediments; localized scour occurs as a result of the narrowing of the watercourse affecting

a short section; and local scour occurs due to the obstruction to the flow by the piles and

abutments.

The location of bridges over water currents favours the deterioration of the materials with

which the structure is built, caused by the permanent presence of water and sediments

transported by rivers. Deterioration mechanisms include corrosion of reinforcing steel

and concrete wear in reinforced concrete structures, corrosion of metallic parts on metallic

bridges and deterioration of the elements with which masonry bridges are built.

The accumulation of debris has been the cause or part of the set of causes of the failure

of many bridges. Owing to this accumulation, the hydraulic capacity of the bridge

decreases, the water level upstream of the bridge and the flow velocity increases and the

flow patterns change. The increase in water levels increases the hydraulic loads on the

structure, the increase in speeds favours erosion processes and the change in flow patterns

can generate strong lateral currents and, consequently, large local scour (FHWA, 2005).

The problems generated in bridges by the instability of watercourses are due to

morphological changes in them and have been the cause of the failure of many of such

structures (Johnson, 2005). These problems could also be considered as caused by scour

and can be reflected in phenomena such as a widening of the channel, a lateral migration

or a cut by meanders that can affect the structure.

5.3 Methodology

According to equation 1.2 the risk can be calculated by means of the statistical integral

of the product of the flood hazard by the vulnerability. In this methodology the risk

indicates the probability of annual failure and the vulnerability indicates the probability

of failure at the occurrence of the magnitude event y, therefore, its value fluctuates

between 0 and l. The process by which the hazard, the vulnerability and the risk are

obtained is described in the following sections

5.3.1 Hazard

The flood hazard corresponds to the probability of occurrence of a potentially damaging

event, considering that the damage could occur because there are elements exposed to

such flood (Schanze, 2006). According to Salazar (2013), this type of event is physically

characterized by indicators of its magnitude or intensity.

To quantify the hazard of a bridge regarding floods, consideration must be given to the

fact that the hydrodynamic actions generated on the structure and the erosive phenomena

that cause changes in the cross section of the river are proportional to the magnitude of

such floods, since with more intense floods, stronger impacts are expected both in the

bridge and in the cross section of the river. Considering that the structure of a bridge can

be affected by the increase in both water levels and flow velocity, in this study the

magnitude of the floods was established by the maximum discharge, as it implicitly

considers these two parameters.


54

In order to define the hazard, the cross section of the flow was divided into four bands

(see Figure 5.1): the first band covers from the level of the thalweg of the channel to the

level reached by a discharge such that it does not generate damage to the structure and

whose magnitude could be similar to the magnitude of the dominant or equivalent

discharge; in this methodology, the level reached by this discharge has been labelled Tmin.

The second band is located between the level of the Tmin and the level reached by the

discharge corresponding to 66% of the full-bank discharge. The third band is located

between the level that reaches the discharge corresponding to 66% of the full-bank

discharge and the full-bank level. The fourth and last band is located above the full-bank

level.

Figure 5.1 Scheme representing the bands into which the cross section of a watercourse

is divided for the purpose of the magnitude of a flood

It is considered that the discharges located in the first band (low discharges) are below

the threshold from which important erosive actions would be generated in the cross

section, so its effect on the stability of the structure is quite small. The potential impact

of the flood on the structure increases as the magnitude of the discharges in the second

and third bands increases, in such a way that the full-bank discharge would have an impact

close to the maximum potential impact; this is due to the fact that once the river has

overflowed, the discharges grow with no significant increase in flow velocity and depth

(Vide, 2003). Owing to this, in the fourth band the destabilizing effect on the structure is

expected to not be much greater than that which would be produced with full-bank

discharges.

In this methodology, hazard is defined as the probability of the discharge being in each

of the four bands into which the cross section was divided.

5.3.2 Vulnerability

In determining the vulnerability of a bridge, it should be noted that during a flood the

degree of affectation of the superstructure may differ from the degree of affectation of the

substructure, whereby the probability of bridge failure is established as the probability of

joint failure of both parts of the structure.

Band 3

Band 2

Band 1

Band 4 Full-bank level

Level reached by the discharge equal to 66% of the full-bank discharge

Level reached by the discharge corresponding to Tmin

Thalweg level


55

The vulnerability of a bridge to flooding is determined by several factors, such as the state

of the structure, the stability of the stream channel in which it is located, the capacity of

the bridge to accumulate debris and the deterioration of the structure due to its age and

the environment in which it is located.

In this study, a base vulnerability of the substructure and superstructure was first and

separately identified. This base vulnerability considers only their condition and integrity.

Second, the impact of the remaining aspects was established through multiplication

factors of this base vulnerability, as given in Equations 5.1 and 5.2:

𝑉𝑏 = 𝑉𝐵𝑏 𝐹𝑠 𝐹𝑑 𝐹𝑡 [5.1]

𝑉𝑠 = 𝑉𝐵𝑠𝐹 𝑑𝐹𝑡 [5.2]

where:

Vb = Vulnerability of the substructure

VBb Base vulnerability of the substructure

Vs = Vulnerability of the superstructure

VBs Base vulnerability of the superstructure

Fs = Multiplication factor due to the stability of the stream channel

Fd = Multiplication factor due to the potential of the structure to accumulate debris

Ft = Multiplication factor due to deterioration of the structure

The multiplication factor due to the stability of the stream channel is not included in

Equation 5.2 because, with a few exceptions, this aspect is unlikely to affect the

superstructure. The different components of these equations are described in more detail

in the following sections.

5.3.2.1 Base vulnerability

The base vulnerability of the structure is a function of various aspects that determine the

susceptibility of its current condition and integrity to flood damage. According to Vallés

(2011), the most relevant of these factors are the following:

Type of foundation. It could be superficial (the most susceptible), semi-deep or deep

(the least susceptible).

Structural specifications of the bridge. It refers to the materials with which the bridge

is built and the various types of abutments, piles and decks.

Condition of the structure. The substructure and superstructure units could suffer

severe or minor damage.

Scour. It could be severe, advanced, moderate, incipient or non-existent.

Material of the watercourse in the vicinity of the abutments and piles. It could be, for

example, alluvial, solid terrain or rock.

To estimate the base vulnerability of the structure, an assessment of the condition of the

structure must initially be made based on the assessment of the factors listed above. In

this study, this assessment was made through the procedure proposed by Vallés et al.


56

(2011), which classifies structures by assigning a code between 0 and 9 based on the

assessment of these factors. The better the condition of the structure, the greater the

corresponding code, such that 0 corresponds to bridges that have already failed and 9 to

bridges in excellent condition (Table 5.1).

In order to classify the structure, each of the units that make up the structure must be

independently evaluated and classified. The classification of the bridge shall correspond

to the classification of the structural unit in the worst condition.

To each one of the codes in which the structure can be classified correspond vulnerability

values that depend on the bands into which the cross section was divided, since

vulnerability increases as the intensity of the flood increases. Since band 1 corresponds

to discharges below the discharge from which the cross section and/or structure may be

affected, the vulnerability for this band is zero. The vulnerability values defined for the

remaining bands and each of the classification codes are given in Table 5.1. The values

presented in this table correspond to the probability that the bridge will fail when the

considered flood occurs.

Table 5.1 Base vulnerability of the substructure (VBb) and superstructure (VBs)

of a bridge in floods adopted in this proposal

Condition of the structure Vulnerability

VBb VBs

Cod. Description Band Simply

supported Embedded

2 3 4

0 Failure. Reconstruction actions are

required 1.0 1.0 1.0 1.0 1.0

1 Failure imminent. Great deterioration,

loss of section, great scour 1.0 1.0 1.0 1.0 1.0

2 Critical. Very significant deteriorations

of main elements. Bridge closed 0.5 0.8 0.9 0.9 0.8

3 Seriously deficient. Danger of total

collapse 0.3 0.6 0.7 0.8 0.7

4 Poor. Loss of section. Significant scour.

Affects fundamental elements 0.15 0.4 0.6 0.6 0.5

5 Acceptable. Deterioration and minor

scour. Bed instability 0.075 0.15 0.2 0.3 0.2

6 Satisfactory. Minor deterioration. Little

or no evidence of scour. 0.04 0.1 0.15 0.15 0.1

7 Good. Adequately protected structure

or protection is unnecessary 0.03 0.075 0.1 0.1 0.075

8 Very good. Transversal drainage of

roads or foundations on solid rock 0.005 0.03 0.05 0.05 0.03

9 Excellent. All substructure units are

over avenue Tr 500 years 0.002 0.005 0.01 0.09 0.005

N Not applicable - - - - -


57

5.3.2.2 Stream channel stability

The lack of horizontal and vertical stability of a stream channel can lead to the collapse

of important infrastructure works, including bridges. However, despite the potential

negative effects of this phenomenon, to date there are few methods available to assess the

degree of stability of a river (Yanmaz et al., 2007; Johnson et al., 2011).

Determining the stability of a water current should include an assessment of the existing

and potential processes of bed aggradation and degradation, cross section widening and

lateral migration. This assessment must take into account both the local characteristics (in

this case, the location of the bridge) and those of the entire watershed.

Factors to be considered at basin level include land use (natural, light or highly

anthropized, etc.), flow regime (e.g. perennial, intermittent, rapid, slow, etc.), and type of

watercourse (straight, meandering or braided). The factors of the channel to be considered

in the place where the bridge is located include in particular the slope, granulometry of

the bed material (e.g. cohesive material, granular material, pebbles, etc.), the degree of

confinement of the channel, the presence of bars and obstructions to the flow, the

orientation of the structure with respect to the flow, the presence of vegetation on the

banks and the floodplain, the state and inclination of the banks and the characteristics

(e.g. concrete works, bioengineering works, gabions, etc.) and condition (good, seriously

deteriorated, minor damage, etc.) of the protection measures.

In this methodology, stream channel stability is determined by the most unfavourable

condition obtained by implementing the procedure proposed by Johnson (2005) and by

evaluating the condition of the channel by means of item 61 of FHWA guide PD-96-001

(FHWA, 1995). The method proposed by Johnson (2005) corresponds to an improvement

of a methodology previously proposed by Johnson et al. (1999). This procedure seeks to

establish the general stability of the stream channel by evaluating the following 13

parameters: watershed and floodplain activity and characteristics, flow habit, channel

pattern, entrenchment/channel confinement, bed material, bar development, obstructions,

bank soil texture and coherence, bank slope angle, vegetative or engineered bank

protection, bank cutting, mass wasting or bank failure, upstream distance to bridge from

meander impact point and alignment (Johnson, 2005).

Johnson (2005) assigns each of these 13 parameters a value between 1 and 12, with a

rating of 1 for the best possible rating and 12 for the worst. The sub-ratings are added

together to obtain a final rating, which varies between 13 and 156 and provides an overall

assessment of the stability of the current.

Data item 61 of the FHWA guide PD-96-001 (FHWA, 1995) allows an evaluation of the

stability conditions of the sector in which the bridge is located, evaluating parameters

different from those considered by Johnson (2005). This item defines the stability of the

watercourse by establishing a scale of between 0 and 9, with 0 as the worst condition and

9 as the best condition. Since the scales used by Johnson (2005) and FHWA (1995) are

different from each other, Johnson et al. (2011) made an equivalence between these two

scales to establish the general stability of the water current, which could be classified as

excellent, good, acceptable or poor (Table 5.2).


58

Considering that, as already noted, the two methods used evaluate different parameters,

it is possible to obtain two different stability conditions for the same current. As a result,

in this methodology the stability of the stream channel is determined by the most

unfavourable condition, that is, by the one that indicates the least stability. Thus, the

proposal of this methodology for the multiplication factor corresponding to the stability

of the stream channel that affects the base vulnerability (Equation 5.1) ranges from 1.0

for an excellent stability condition to 1.3 for a poor stability condition (Table 5.2).

Table 5.2 Proposed values of the base vulnerability multiplication factor due to the

stability of the water current (Fs)

Stability of the stream

channel

Johnson scale

Channel condition

Item 61 of the FHWA coding system Fs

Rating Description Cod. Description

> 120 Poor

0 Bridge closed because of channel failure.

Replacement necessary

1.3 1 Bridge closed because of channel failure.

Corrective action may put back in light service

2 The channel has changed to the extent the bridge

is near a state of collapse

86 -120 Acceptable

3 Bank protection has failed

1.2 4 Bank and embankment protection is severely

undermined

5 Bank protection is being eroded

50 – 85 Good 6 Bank is beginning to slump

1.1 7 Bank protection is in need of minor repairs

12 – 49 Excellent

8 Banks are protected or well vegetated

1.0 9

There are no deficiencies which affect the

condition of the channel

- - N Not applicable -

5.3.2.3 Potential of the structure to accumulate debris

The accumulation of debris in bridges is a widespread problem that has been among the

causes of the collapse of several structures of this type. The accumulation of debris can

generate several problems, including the decrease in transport capacity across the bridge,

the increase in local and localized erosion, the increase in hydraulic loads and the

generation or increase in flooding upstream of the structure (FHWA, 1997).

According to NCHRP (2010), the potential of the structure to accumulate debris is a

function of: (i) the potential of the upstream watershed of the structure to produce debris

and the capacity of the stream to transport it; (ii) the location of the piles and abutments

of the bridge with respect to the watercourse, which could be protected (forest area or

with other obstructions that could trap the debris upstream of the bridge), in the floodplain

and top of the bank (areas without trees or prone to being left without trees), in the channel

or in the sector of the cross section in which the transport of debris is concentrated; (iii)


59

the type of pile of the bridge, which could be solid or with openings; and (iv) the

dimensions of the spans between the different elements of the bridge and the cross section.

FHWA (2005) establish the potential of the piles and spans to accumulate debris through

the information given in Table 5.3, which is based on the evaluation of the above aspects.

In order to establish the potential of the bridge to accumulate debris, the potential of each

pile and each span for such accumulation must be determined independently and then the

most unfavourable option, i.e. the highest potential, must be selected.

Table 5.3 also shows the values proposed in this methodology for the base vulnerability

multiplication factor due to the potential of the structure to accumulate debris (Equations

5.1 and 5.2).

Table 5.3 Proposed values of the base vulnerability multiplication factor due to

the potential of the structure to accumulate debris (Fd)

Element of the structure

Location

Potential for

debris

transport and

delivery

Potential to

accumulate

debris

Fd Type Classification

Pile

- Sheltered -

Low 1.0 Solid Top bank-Flood plain -

Channel Low

With openings Top bank-Flood plain Low

Solid

Channel High

Medium 1.1

Path of concentrated

debris transport Low

With openings Top bank-Flood plain High

Channel Low

Solid Path of concentrated

debris transport High

High 1.2

With openings



Channel High

With openings Path of concentrated


High-

Chronic 1.3

Span

- Sheltered -

Low 1.0

Width greater than

design log length - -

Width smaller than

design log length

Top bank-Flood plain Low

Channel Low

Width smaller than

design log length



Medium 1.1

Top bank-Flood plain High

Width smaller than

design trunk length Channel High High 1.2

Width smaller than

design log length



High-

Chronic 1.3


60

5.3.2.4 Deterioration of the structure due to its age and the environment in which it

is located

The deterioration of a bridge due to its ageing and the environment in which it is located

increases its vulnerability to flooding. In this methodology, the impact of this

deterioration on vulnerability is established on the basis of the material in which the

structure is built.

Reinforced concrete bridges

In this type of structure, consideration must be given to the deterioration of the concrete

and the reinforcing steel. The location of bridges on water currents favours the

deterioration of the concrete as most of the mechanisms that generate such deterioration

require the presence of high moisture content or liquid water. In fact, attacks on concrete

by dry chemicals are rare (Boyd and Skalny, 2007). The main causes of concrete

deterioration include the alkali-aggregate reaction, abrasion by external agents, frost and

thaw cycles and the attack of sulphates.

The alkali-aggregate reaction refers to the chemical reaction of certain aggregates with

the hydroxyl ions and alkaline components of the cement paste, which generates

expansive reactions, concrete cracking and loss of resistance and elastic modulus (Mehta

and Monteiro, 2006). This reaction requires the presence of moisture, is more severe when

structures are subject to wetting and drying cycles and occurs more rapidly at higher

temperatures. According to Malhotra (2011), when using a similar type of reactive

greywacke aggregate in Cape Province in South Africa, the deterioration of structures due

to this phenomenon occurs after a period of between 4 and 7 years, while in Canada,

where the temperature is much lower, the deterioration usually appears after 15-20 years.

Deterioration due to sulphate attack occurs when the structure is exposed to soil,

groundwater or agricultural or industrial waste containing sulphate ions (Boyd and

Skalny, 2007). The penetration of sulphate into the concrete structure generates expansive

chemical reactions that cause a loss of strength due to the loss of adhesion between the

cement paste and the aggregates (Maes et al., 2012). The degree of deterioration depends

mainly on the concentration of sulphate ions in the soil or water that is in contact with the

concrete (Aguirre and Mejía de Gutiérrez, 2013).

External agents, such as the action of the sediments carried by water, ice or waves on a

pile or abutment of a bridge, can generate significant abrasion on the concrete surface,

especially during large floods (Ministerio de Fomento de España, 2012). Ragab et al.

(2012) found average concrete abrasion rates of between 0.2 and 0.8 mm/year in wave`s

repellent blocks of different ages (between 4 and 62 years) built on the northern coast of

the Mediterranean Sea in Egypt.

The ice and water thawing cycles generate a significant deterioration of the concrete, as

the water contained in the pores of the concrete freezes, increasing its volume by

approximately 9%, generating stress forces that cause cracks in and delamination of the

concrete (Mejía and Rodríguez, 1999). The deterioration of the structure depends on the


61

permeability of the concrete, the amount of water available for ice formation, the degree

of saturation of the concrete and the rate at which ice is formed.

Corrosion of reinforcing steel has been the cause of the collapse of many bridges

(Wardhana and Hadipriono, 2003; Concrete Society, 2002) and is mainly due to

carbonation phenomena and chloride attack. Steel corrosion occurs when aggressive

agents (CO2 and chloride ions) enter the cement matrix and reach the metal (Instituto

Mexicano del Transporte IMT, 2001).

Carbonation is due to the entry of CO2 into the concrete from the atmosphere, which is

why urban and industrial environments and environmental pollution favour this process.

Other factors that favour carbonation correspond to inadequate curing, a high

permeability of the concrete and a relative humidity whose ideal values to encourage the

phenomenon are between 50 and 70% (Aguirre and Mejía de Gutiérrez, 2013). According

to El-Reedy (2008), the diffusion rate of carbonation can be of the order of 0.25 mm/year

and 1 mm/year for good and poor quality concretes, respectively. According to Andrade

(2007), the corrosion propagation period up to an acceptable minimum value due to the

carbonation phenomenon would be between 20 and 40 years assuming a corrosion rate of

5 µm/year.

The chloride attack can come from two main sources: the first is chloride ions in the

concrete, e.g. due to aggregates or contaminated water, seawater or additives with high

chloride content. In the second source, the chlorides come from outside due to exposure

to marine environments, the use of de-icing salts and chemicals containing chlorides (El-

Reedy, 2008). The advancement of chlorides in concrete is related to its permeability

(Aguirre and Mejía de Gutiérrez, 2013). According to Andrade (2007), in this case the

maximum period to be considered until the corrosion reaches an acceptable limit value is

5-10 years, since in cases of localized corrosion the deterioration of the structure can be

significant. For example, Costa and Appleton (2002) reported corrosion rates of 7

µm/year due to chloride attack on a deteriorated bridge near the sea in Portugal.

According to Andrade (2007), for service lives of more than 75 years or when the

structure is located in very aggressive environments, reinforced concrete requires a

minimum quality and coverage thickness or even additional protection methods to

prevent corrosion.

The multiplication factors of the base vulnerability due to the deterioration of bridges

built in reinforced concrete are given in Table 5.4.

Metallic Bridges

The main durability problem of this type of structure is represented by the corrosion of

the metallic elements, which are very sensitive to climatic and environmental factors. The

rate of corrosion depends on the temperature, humidity and aggressiveness of the air in

contact with the structure (Matute and Pulido, 2012). The most adverse conditions

correspond to those in which structures are exposed to marine environments, in direct

contact with water for long periods of time, exposed to permanent humidity or industrial


62

atmospheres or contaminated with aggressive agents such as SO2 (Sánchez, 2012;

Ministerio de Fomento de España, 2012).

Several strategies are available to counteract or control corrosion, including the

application of a coating (zinc, aluminium, etc.), paints that act as a physical barrier and

the use of corten steels, which first appeared in civil and architectural works in the 1960s

(Sánchez, 2012).

The base vulnerability multiplication factors adopted as a consequence of the

deterioration of metal bridges are given in Table 5.4.

Masonry Bridges

These structures have high strength and rigidity, which gives them very long service lives.

Their strength is defined by the mortar, which has a much lower strength than that of

stone materials (Sharhosis, 2016).

The deterioration of these structures is caused mainly by water, sediments transported by

rivers, the effect of traffic and unfavourable environmental and climatic conditions such

as those found in urban and industrialized areas. There are also more problems with

bridges built with bricks than with bridges built with stone materials (Ministerio de

Fomento de España, 2012)

The values of the base vulnerability multiplication factor adopted in this methodology

due to the deterioration of masonry bridges are given in Table 5.4.

Table 5.4 Proposed values of the base vulnerability multiplication factor due to

the deterioration of the bridge structure (Ft)

Specifications of the Structure

Ft Type Location

Age

(years)

Reinforced Concrete

Non-marine environments and

no de-icing salts

0-20 1.0

20-40 1.1

40-75 1.2

>75 1.3

Marine environments or de-icing

salts

0-10 1.0

10-20 1.1

20-40 1.2

>40 1.3

Metallic

Rural or urban environment <50 1.0

>50 1.2

Marine or industrial environment <50 1.1

>50 1.3

Masonry

bridges

Stone

materials

Rural environment - 1.0

Urban or industrial environment - 1.1

Ceramic

materials

Rural environment - 1.2

Urban or industrial environment - 1.3


63

5.3.3 Risk of bridge failure due to river floods

The risk of bridge failure due to river floods is calculated as the product of the probability

of a flood occurring multiplied by its possible negative consequences on the structure. By

solving Equation 1.2 discretely, considering that the substructure and superstructure can

fail independently, one obtains that the risk of failure of a bridge corresponds to:

[5.3]

where:

Vbi = Vulnerability of the substructure for flows located in the i band of the cross section

∆Pi = Probability of discharges occurrence in band i

Vs = Vulnerability of the superstructure

Ps = Probability of the flood reaching the superstructure

By replacing Equations 5.1 and 5.2 in Equation 5.3 one has:

[5.4]

In determining risk, only the vulnerability and the probability of discharges occurrence in

bands 2, 3 and 4 are considered; information related to band 1 is not considered since, as

already noted, the discharges in this band are lower than the discharges corresponding to

the Tmin, so they do not have a negative impact on the structure. It should also be noted

that the maximum value of the product of the base vulnerability, both of the substructure

and of the superstructure, by multiplication factors may not exceed the value of 1.

5.4 Application in a case study

The methodology developed was applied to 12 Spanish river bridges, 4 of which were

railway bridges and the others road bridges. Ten of these bridges are still in operation, the

bridge over the Cervera river collapsed in October 2000 and the bridge over the Girona

River failed in October 2007. The information related to the structures and water currents

in which they are located was taken from Vallés (2011). Figure 5.2 shows the location of

these bridges and Table 5.5 shows their main specifications.

58% of the bridges studied are reinforced concrete structures and 42% are masonry

bridges. In terms of size, 25% of the bridges have large dimensions, 50% correspond to

bridges with a span greater than 10 metres and the remaining 25% to pontoons with a

span of less than 10 metres. As far as typology is concerned, it should be noted that 42%

correspond to vault bridges, 25% to arch bridges and 33% to conventional structures

(beams, slabs, etc.).

𝑅𝑖𝑠𝑘 = ∑ 𝑉𝐵𝑏𝑖 𝐹𝑠 𝐹𝑑 𝐹𝑡 ∆𝑃𝑖

4

𝑖=2

+ 𝑉𝐵𝑠 𝐹𝑑 𝐹𝑡 𝑃𝑠

𝑅𝑖𝑠𝑘 = ∑ 𝑉𝑏𝑖 ∆𝑃𝑖

4

𝑖=2

+ 𝑉𝑠 𝑃𝑠


64

Figure 5.2 Location of the bridges to which the methodology was applied

Table 5.5 Specifications of the bridges to which the developed methodology

was applied

Condi-

tion No. River Road

Specifications of the structure Date of

inspection(1) Classification Type No. Span

In

Operation

1 Ambroz A-66 Pontoon L < 10 m Conventional 1 12/03/2010

2 Ebro N-420 Large structure Conventional 7 28/02/2007

3 Eresma SG-020 Large structure Arch 7 23/03/2010

4 Frío N-110 Pontoon L < 10 m Vault 2 09/04/2010

5 Genil A-4 Large structure Conventional 7 13/02/2002

6 Pisuerga Railway Bridge L > 10 m Arch 4 12/12/2007

7 Pisuerga Railway Bridge L > 10 m Arch 4 12/12/2007

8 Segre N-260 Bridge L > 10 m Vault 3 15/07/2008

9 Ucieza Railway Bridge L > 10 m Vault 1 11/12/2007

10 Ucieza Railway Pontoon L < 10 m Vault 1 10/12/2007

Collapsed 11 Cervera CV-132 Bridge L > 10 m Conventional 24 -

12 Girona CV-732 Bridge L >10 m Vault 5 -

(1) Date on which Vallés (2011) performed the field inspection

The determination of the condition of each of the analysed structures, the stability of the

stream channel, the potential of the structures to accumulate debris and their deterioration

were defined according to the guidelines provided in Section 5.3 and are given in Table

5.6. This information made it possible to determine the base vulnerability of the

superstructure and substructure and their multiplication factors, which are given in Table

5.7 (columns six to twelve).

The hazard corresponding to the probability of occurrence of floods was calculated from

information published by the Sistema Nacional Floodplain de Cartografía de Zonas

Inundables (2019). This mapping defines the discharges for floods corresponding to


65

return periods of 2, 5, 10, 25, 100 and 500 years. The probabilities of occurrence (P in

Table 5.7) of the discharges for each of the bands into which the cross section was divided

were interpolated from this information.

Table 5.6 Stability of water currents and condition of the structures of the

bridges analysed

Bridge

condi-

tion No. River

Condition of the

structure Current stability

Poten-

tial to

accum.

Debris

Deterioration of the

structure

Cod. Description

Stability of the

stream channel

Johnson scale

Channel condition

Item 61 FHWA Building

material

Loca-

tion

Age

(years)(1)

Cod. Description Cod. Description

In

operation

1 Ambroz 6 Satisfactory 62 Good 8 Banks are protected or

well vegetated High

Reinforced

Concrete River 50

2 Ebro 4 Poor 55 Good 7 Bank protection is in

need of minor repairs Low

Reinforced

concrete River 30

3 Eresma 5 Acceptable 40 Excellent 8 Banks are protected

or well vegetated Low

Reinforced

concrete River 30

4 Frío 3 Seriously

deficient 59 Good 7

Bank protection is in

need of minor repairs High

Reinforced

concrete River 50

5 Genil 4 Poor 71 Good 6 Bank is beginning to

slump Medium

Reinforced

concrete River 30

6 Pisuerga 4 Poor 45 Excellent 9

There are no

deficiencies which

affect the channel

Low Reinforced

concrete River 50

7 Pisuerga 4 Poor 60 Good 7 Bank protection is in

need of minor repairs Low

Masonry-

ceramics Rural -

8 Segre 3 Seriously

deficient 52 Good 7

Bank protection is in

need of minor repairs Medium

Masonry-

ceramics Rural -

9 Ucieza 4 Poor 49 Excellent 8 Banks are protected or

well vegetated Medium

Masonry-

ceramics Rural -

10 Ucieza 4 Poor 59 Good 6 Bank is beginning to

slump Medium

Masonry-

ceramics Rural -

Collap-

sed

11 Cervera 3 Seriously

deficient 88 Acceptable 5

Bank protection is

being eroded Medium

Reinforced

concrete River 50

12 Girona 3 Seriously

deficient 86 Acceptable 4

Bank and embank-

ment protection is

undermined

Medium Masonry-

ceramics Urban -

(1) Exact information on the age of bridges is not available, so this is approximate.

In order to define the upper limit of band 1, the minimum affectation threshold (Tmin)

corresponded to the flood with a return period of 7 years. This flood corresponds to the

upper limit of the range between 1.5 and 7 years, which, according to Vide (2003),

constitutes the range in which the return periods of the dominant discharges of the Spanish

rivers could fluctuate. The selected value is considered relatively conservative, so the

results obtained are on the safe side.

The risk of failure due to river floods for each of the bridges analysed was calculated

using Equation 5.4. The results obtained are given in the last column of Table 5.7. The

bridges over the Cervera River and the Girona River, which have already collapsed,

present risks of failure of 0.11 and 0.14, respectively, which are very high values and


66

indicate the need for urgent intervention to guarantee the integrity of the structure. This

result in some way validates the proposed methodology and could be indicating that this

method takes into account the most important elements to be considered when

establishing the risk of bridge failure in the event of flooding.

Table 5.7 Risk of failure of bridges located on Spanish roads due to river floods

Condition

of

bridge No. River

QB(1)

(m³/s)

Base vulnerability of structure VB/

Probability of occurrence of flows P

Multiplication

factors

Risk

(annual

failure

proba-

bility)

Parameter

VBb

VBs Fs Fd Ft Bands Cross Section

2 3 4

In

operation

1 Ambroz 383 VB 0.04 0.10 0.15 0.10

1.1 1.3 1.3 0.01 P 0.24 0.01 0.00 0.00

2 Ebro 8798 VB 0.15 0.40 0.60 0.50

1.1 1.0 1.1 0.04 P 0.21 0.03 0.01 0.01

3 Eresma 2724 VB 0.05 0.15 0.20 0.20

1.0 1.0 1.1 0.01 P 0.25 0.00 0.00 0.00

4 Frío 39 VB 0.30 0.60 0.70 0.70

1.1 1.3 1.3 0.09 P 0.25 0.00 0.00 0.00

5 Genil 1522 VB 0.15 0.40 0.60 0.50

1.1 1.1 1.1 0.09 P 0.13 0.07 0.05 0.05

6 Pisuerga 1207 VB 0.15 0.40 0.60 0.50

1.0 1.0 1.3 0.03 P 0.25 0.00 0.00 0.00

7 Pisuerga 648 VB 0.15 0.40 0.60 0.50

1.1 1.0 1.1 0.03 P 0.23 0.02 0.00 0.00

8 Segre 323 VB 0.30 0.60 0.70 0.70

1.1 1.1 1.1 0.10 P 0.17 0.05 0.03 0.03

9 Ucieza 94 VB 0.15 0.40 0.60 0.50

1.1 1.1 1.1 0.06 P 0.16 0.07 0.02 0.02

10 Ucieza 710 VB 0.15 0.40 0.60 0.50

1.0 1.1 1.1 0.08 P 0.11 0.11 0.03 0.03

Collapsed

11 Cervera 300 VB 0.30 0.60 0.70 0.70

1.3 1.1 1.3 0.11 P 0.19 0.02 0.03 0.03

12 Girona 147 VB 0.30 0.60 0.70 0.70

1.3 1.1 1.3 0.14 P 0.12 0.05 0.08 0.08

(1) QB = Discharge at full section

50% of the bridges analysed still in operation show a high risk of failure due to floods

(between 0.05 and 0.10), which suggests that they require immediate attention; in

particular, the bridge over the River Segre presents the most adverse conditions with a

0.10 risk. 30% of the bridges analysed show a medium risk (between 0.03 and 0.04),

indicating that action must be taken to improve this condition in the short term. The

remaining 20% return a low risk of failure (equal to 0.01), suggesting that no

extraordinary intervention is required on these structures and that the routine inspection

and maintenance plan must be continued.

Multiplication factors for stream channel stability, potential for debris accumulation and

structure deterioration can lead to a significant increase in the base vulnerability of the

structure. In the case of the bridges on the Ambroz, Frío, Cervera and Girona rivers, this

increase was almost 86%. With the exception of the bridge over the Ambroz River, the

methodology indicates that these bridges present or presented a high risk of failure.


67

It is also generally observed that, as expected, in rivers where there is a greater probability

of finding discharges close to or higher than full-bank, the risk of failure of the structures

increases. The River Frío seems to escape this trend, since although the probability of

reaching high flows is low, the structure presents a high risk of failure.

5.5 Sensitivity analysis

Considering that the main objective of this methodology consists of ordering the level of

intervention required by a set of bridges, that the values established for vulnerability are

associated with a high degree of subjectivity and that the value of Tmin is uncertain, the

sensitivity of the risk to the values of vulnerability and Tmin was determined.

This analysis made it possible to establish the extent to which the risk values and the order

of the bridges vary when these parameters are modified. The analysis is local and

univariate. Accordingly, on the one hand, Tmin values equal to 1.5, 4, 15 and 50 years

were adopted; the value of 1.5 years corresponds to the lower limit of the range in which,

according to Vide (2003), the return periods of the dominant discharges of the Spanish

rivers could fluctuate, while the value of 4 years corresponds approximately to the

average value of this range. On the other hand, the effect of vulnerability was studied

through the modification of vulnerability, for which its value was increased by 50 and

100% and decreased by 25 and 50%.

The results obtained by performing this test are given in Table 5.8, in which the bridges

studied are classified according to the values of risk obtained during the implementation

of the methodology. The analysis of this information allows us to conclude that the

threshold above which both the structure and the watercourse are considered to be

affected due to the action of the flood has a high influence on risk values, since these

increase on average by almost 350 and 150% when Tmin values of 1.5 years and 4 years,

respectively, are considered; and they decrease on average by 43 and 78% when

considering Tmin values of 15 and 50 years, respectively. However, the order of the rivers

when considering their risk values remains without major modifications since, when

considering a Tmin of 50 years, the order remains the same; when considering a Tmin of 15

years, only the Frío and Genil rivers would exchange positions; and when considering

Tmin values of 1.5 and 4 years, only the Frío and Segre rivers would exchange positions.

When modifying the values of vulnerability, a similar behaviour to that obtained when

modifying the values of Tmin is observed, since, as expected, on average the risk increases

by 67 and 36% when vulnerability is affected by factors of 2.0 and 1.5 and, similarly, it

is reduced by 21 and 45% when vulnerability is affected by factors of 0.75 and 0.5,

respectively. As with the Tmin, the order of the bridges does not undergo major variations

since, when the vulnerability increases by 50%, the order remains the same; when

duplicating the vulnerability, the only change observed is that the River Ucieza would be

located after the Genil and Frío Segre rivers; and when reducing the vulnerability by 25

and 50%, only the bridges over the Genil and Frío rivers would exchange positions.


68

Table 5.8 Fail Risk Sensitivity Test

Bridge

condition No. River

Risk (probability of failure/year)

Proposed

Methodo-

logy

Sensitivity analysis

Tmin (years) Vulnerability

1.5 4 15 50 Method.

*2.0

Method.

*1.5

Method.

*0.75

Method.

*0.5

In

operation

1 Eresma 0.008 0.037 0.014 0.004 0.001 0.016 0.012 0.006 0.004

2 Ambroz 0.013 0.051 0.021 0.007 0.003 0.025 0.019 0.009 0.006

3 Pisuerga 0.028 0.130 0.049 0.013 0.004 0.056 0.042 0.021 0.014

4 Pisuerga 0.035 0.130 0.054 0.021 0.011 0.068 0.052 0.026 0.018

5 Ebro 0.044 0.139 0.063 0.030 0.014 0.079 0.062 0.034 0.023

6 Ucieza 0.064 0.168 0.085 0.042 0.017 0.110 0.090 0.049 0.034

7 Ucieza 0.079 0.174 0.098 0.044 0.018 0.136 0.109 0.061 0.042

8 Genil 0.086 0.191 0.108 0.055 0.018 0.127 0.111 0.069 0.049

9 Frío 0.087 0.379 0.146 0.044 0.018 0.132 0.122 0.067 0.045

10 Segre 0.100 0.309 0.143 0.060 0.020 0.143 0.122 0.080 0.057

Collapsed 11 Cervera 0.105 0.398 0.165 0.063 0.020 0.143 0.129 0.089 0.065

12 Girona 0.135 0.427 0.195 0.067 0.020 0.143 0.140 0.124 0.095

5.6 Final Remarks

The developed methodology was applied to 12 river bridges located on Spanish roads.

The results obtained were satisfactory, which could indicate that the proposed method

takes into account the most important elements to be considered when establishing this

type of risk.

The implementation of the methodology in the selected case study indicates that only

20% of the bridges currently in operation return a low or acceptable risk and therefore do

not require special action, while the remaining 80% require interventions in the medium

and short term.

Given its ease of implementation and the relatively low demand for information needed

for its application, the proposed method could become a support tool for decision-makers

responsible for the design, maintenance, repair and reconstruction of bridges. The

adequate and timely implementation of this method would make it possible to detect alerts

on the state of the structure in a reasonable time and at a reasonable cost.

Chapter 6, Conclusions and futures research lines

69

6 CONCLUSIONS AND FUTURES RESEARCH LINES

6.1 Conclusions

In this research, a methodology was developed to estimate the risk that river floods

generate on a road network in three different scenarios, which corresponded to

floodplains, stream crossings and bridges. The procedure developed allows calculating in

the first two scenarios the average annual number of vehicles at risk due to flooding when

they are driven or parked at a given area or at stream crossings, which can correspond to

fords, vented fords or bridges. The third scenario allows establishing the probability of

annual failure of bridges due to floods. In the three scenarios, which allowed studying

several of the elements that may be affected during floods, a common methodology was

used based on the statistical integration of the flooding hazard and the vulnerability of the

exposed elements.

Given the importance of vehicles and transport systems for society, determining the

vehicle instability risk due to flooded rivers is an extremely important factor for planning,

designing and managing roads. Determining this risk can also allow suitable efforts and

resources to be assigned to invest in transport systems’ sustainability. Hence

implementing this methodology can help to reduce negative effects before and during

flooding events, which is extremely helpful for those organizations in charge of urban

planning and civil protection to design and take actions that cushion the negative effects

of flooding.

6.1.1 Vehicle stability models during floods

In recent years several authors have proposed different models to establish vehicle

stability thresholds during a flood event, most of them have considered that vehicles are

watertight, some have considered that water can enter the vehicles exposed to flooding

and others allow considering both watertightness and non-watertightness conditions.

Also, the criterion to determine the stability threshold varies among the studied stability

models. These differences in the way of approaching vehicle watertightness, the decision

criterion adopted to determine the stability of the cars and, more importantly, different

driving factors, lead to quite a wide range of stability thresholds as obtained by the various

models.

The comparison of the studied stability models with the experimental data suggests that

most stability models seem to be conservative for low flow velocities and that the models

proposed by the DIPNR (2005), Ausroads (2008), Kramer et al. (2016), Martínez-

Gomariz et al. (2017) for high velocities and the AR&R (2011) and Smith (2017) for

speeds over 3.0 m/s seem to be excessively conservative. Additionally, it could be

observed that the stability models proposed by Moore and Power (2002) for small

passenger cars and by Oshikawa and Komatsu (2014) establish limits of stability

threshold higher than the combinations of velocity and depth for which several of the

studied experimental cars lost their stability. Because of this, these models could be

unsafe for certain types of car.


70

The stability model proposed by Arrighi et al. (2016a) seems to provide an acceptable fit

for the experimental data for medium and high velocities while the model proposed by

Martínez-Gomariz seems to have a similar goodness of fit for the measured data in the

case of medium velocities. It should be highlighted that these models are the only ones

that allow calculating a stability threshold for any vehicle.

All the stability models have made simplifications in the experimental part or in the

theoretical deduction of the stability thresholds that can influence the final result. Due to

this, the experimental data and the stability models present excessive sample dispersion.

This is why it is necessary to conduct new researches that focuses on to overcome these

simplifications and to try to standardise the decision criteria which should be adopted to

define stability thresholds for vehicles of different characteristics.

6.1.2 Assessing the risk of vehicle instability due to flooding

A methodology that allows vehicle instability risk estimates to be made during flooding

while being driven or parked at a given point on the territory was developed. This

methodology estimates the annual mean number of at-risk cars by classifying these by

vehicle type and being representative of the vehicle fleet in any given area.

Efforts were made to develop a rigorous methodology from the statistical point of view,

but a relatively simple one to implement. To determine the vehicle instability risk, it is

necessary to have the water depths and maximum velocities of floods, which may affect

the area of interest, as well as the basic characteristics of the vehicles in this area. The

instability hazard is determined according to a stability function of partially submerged

vehicles. Vehicles’ vulnerability is established by combining exposure and susceptibility;

exposure is calculated by multiplying vehicle density by each vehicle’s proportion in the

fleet; susceptibility is determined with the damage function, which takes values of 0

(unharmed vehicles) and 1 (100% vehicle damage) depending on whether the vehicle is

stable or not. Finally, the risk at each point is obtained by doing a numerical

approximation of the statistical integral of the instability hazard and vehicles’

vulnerability.

The number of vehicles at risk for overflowing rivers can be sensitive to the return period

corresponding to the event in which the area of interest starts to flood, which is known as

Tmin in this methodology. The most accurate estimation for this return period would allow

values for at-risk vehicles to be obtained, which would come closer to real values.

Representation of the vehicle fleet in the flood-prone area significantly impacts the

overall value of the vehicles at risk for instability. Therefore, any mistaken or inaccurate

selection of the vehicles that represent the vehicle fleet may distort the results.

6.1.3 Determining the vehicle instability risk in stream crossings

A methodology that allows instability risks due to floods to be estimated for vehicles

driving through stream crossings was developed. The stream crossing may correspond to

fords, vented fords or bridges. With bridges, this methodology can be used for

hypothesising that bridge structures would not fail during floods. The calculated risk


71

corresponded to the annual mean number of vehicles that would float or be dragged by

the flow.

With this methodology, instability risk was calculated by combining hazard and

vulnerability. To determine hazard, the stability function of partially submerged vehicles,

the geometric characteristics of vehicles, the hydrodynamic characteristics of floods

(water depths and velocities) and the probability of them occurring were employed.

Vulnerability was determined by combining exposure and susceptibility, which are

respectively established with the exposure and damage function Finally, risk was

calculated by the discrete solution of the statistical integral of the product of hazard by

vulnerability.

The number of vehicles at risk for instability due to floods proved extremely sensitive to

the magnitude of the limit water depth from which drivers would decide to stop driving

through flooded zones. The magnitude of the risk increased as drivers would take poorly

conservative attitudes; that is, if decided to drive through higher water levels.

Determining a safe limit water depth, that is, one associated with a low risk level, can

help to encourage drivers’ good behaviour.

The number of vehicles at risk for instability can also vary according to the extent that

vented fords are obstructed. This risk can significantly increase when these stream

crossings are obstructed or possibly blocked. To avoid this risk increasing, vented fords

and periodically performing maintenance tasks should minimise this possibility.

6.1.4 Risk assessment of bridge failure due to river floods

A methodology was developed to evaluate the risk of failure of bridges due to river floods.

The methodology is probabilistic with a detailed determination of the vulnerability to

bridge failure. The end result is an annual probability of failure, at least in theory. This

uncertainty disappears to a large extent when the results are used for planning the level

of intervention required for a given set of bridges which, for example, could belong to the

same geographical or administrative area. Accordingly, the methodology makes it

possible to identify the bridges that are most at risk, which would require much more

immediate intervention than bridges with medium and low risk.

The information needed to implement the methodology is of two types: vulnerability and

frequency of floods. Vulnerability can be obtained through field visits and by analysing

other normally available sources of information, such as aerial photographs of both the

bridge and the watercourse downstream and upstream and the watershed upstream of the

structure. The frequency of floods can be established through available discharges

information.

To determine vulnerability, certain successfully implemented methods available in the

literature are used to establish the state and integrity of the bridge, the potential of the

bridge to accumulate debris and the stability of the stream channel. The strategic

implementation of these methods, together with other analyses, makes it possible to

reliably establish the risk of bridge failure during floods.


72

The risk values are in direct function of a discharge from which both the structure and the

watercourse begin to be affected by the action of the flood, which in this methodology

has been called Tmin. Therefore, in order to achieve realistic results, this discharge must

be obtained as accurately as possible.

The hydrology of the watercourses in which the bridge is located plays an important role

in determining the risk to which the structure is subjected, since the greater the probability

of large floods, the greater the susceptibility of the structure to damage and, therefore, the

greater the risk of failure.

6.2 Futures research lines

With regard to the vehicle stability models, in order to reduce the sample dispersion of

the experimental data and the stability models, research should be carried out with the

following objectives:

Accompanying the laboratory experiments with the development of mathematical

modelling of the vehicle-flow interaction, similar to that done by Arrighi et al. in

2015, since this can contribute to a better understanding of the hydrodynamic

phenomena that cause vehicle stability loss.

Trying to standardize the decision criterion that must be adopted to define the

stability thresholds. The aspects that have a greater impact on the stability of the

vehicles should be better identified and laboratory tests and theoretical analyses

should be carried out with greater emphasis on these aspects.

Performing more experiments on a representative number of vehicles of various

characteristics, including the most vulnerable ones in each car category. Also, some

kind of safety factor could be considered.

Establishing the friction coefficients between the tyres and the surface by conducting

tests with real-scale vehicles and variable water depths. These tests should be carried

out considering different surface materials and tyres in different wear conditions.

Carrying out experiments at 1:1 scale in which the vehicles lose their stability. Since

making these measurements in laboratory flumes is very complex (because very large

flows and huge flumes would be required), at least these tests could be performed in

tanks with water at rest to study the flotation and leaking of water inside the vehicles,

increasing the number of experiments done by Kramer et al. in 2016 and Smith et al.

in 2017. In order to include the full-scale flow velocity, experiments could be carried

out downstream of dams, as also suggested by Xia et al. in 2011. This research could

be difficult to accomplish due to the environmental legislation.

Regarding the methodology to calculate the risk of vehicle instability and bridge failure,

it is recommended to carry out researches that focus mainly on the following aspects:

Establishing stability functions for partially submerged cars that consider moving

vehicles. This is because the magnitude of the flows that generate the destabilization


73

of the vehicles at rest could differ from the magnitude of the flows that cause the loss

of stability of the moving vehicles.

Studying carefully the factors that influence drivers' decision-making when driving

through flooded areas. In addition to the depth, factors such as, for example, the

velocity of the flow and the extent of the flooded area can affect drivers' decisions in

aspects such as slowing down or stopping the car.

Studying the impact of the variation of vehicular traffic throughout the day in the risk

of vehicles instability. Daytime traffic can vary significantly of the nighttime traffic

and this can lead to significant variations in the risk value to which cars are subject.

Studying the uncertainty associated with the calculated risk values for both vehicles

and bridges. Several parameters are involved in the process of obtaining the risk,

each of which has a certain uncertainty, so the risk finally obtained also has an

associated uncertainty. The quantification of this uncertainty would indicate the

degree of reliability of the calculated risk values.

Considering the vulnerability of vehicles and vehicular traffic in the calculation of

the risk of bridges failure. Other ways of weighing the importance of bridges could

also be considered, such as the economic impact that the failure of these structures

would generate and the cost of repairing or rebuilding them.

Other aspects that should also be studied are the following:

Analysing the possibility of obtaining from the morphological characteristics of the

basin the necessary parameters to establish the flood hazard. This would decrease the

amount of information needed to calculate the risk of vehicle instability due to

flooding.

Defining the impact that the duration of the flood and the circulation of vehicles have

on the risk values in urban areas. Depending on the duration of the flood, the density

of vehicles moving could vary over time and this would lead to changes in the value

of risk.

Making a more detailed definition of the damage function of vehicle due to flooding.

Even though vehicles lose their stability, the damage may not be 100%. The degree

of damage could, for example, be a function of the topography of the terrain, the

direction of flow circulation and the variation in depth and flow velocity.

74

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